feature(Analysis/LocallyConvex/Polar): Bipolar theorem#20843
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feature(Analysis/LocallyConvex/Polar): Bipolar theorem#20843
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PR summary 8b2141b23d
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Analysis.Normed.Module.Dual | 1872 | 1868 | -4 (-0.21%) |
Import changes for all files
| Files | Import difference |
|---|---|
6 filesMathlib.Analysis.Calculus.Gradient.Basic Mathlib.Analysis.InnerProductSpace.Dual Mathlib.Analysis.InnerProductSpace.LaxMilgram Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology Mathlib.Analysis.Normed.Module.Dual Mathlib.Analysis.Normed.Module.WeakDual |
-4 |
77 filesMathlib.Analysis.CStarAlgebra.ContinuousLinearMap Mathlib.Analysis.CStarAlgebra.Matrix Mathlib.Analysis.Convex.Cone.InnerDual Mathlib.Analysis.Fourier.RiemannLebesgueLemma Mathlib.Analysis.InnerProductSpace.Adjoint Mathlib.Analysis.InnerProductSpace.JointEigenspace Mathlib.Analysis.InnerProductSpace.LinearPMap Mathlib.Analysis.InnerProductSpace.Positive Mathlib.Analysis.InnerProductSpace.Rayleigh Mathlib.Analysis.InnerProductSpace.Spectrum Mathlib.Analysis.InnerProductSpace.TwoDim Mathlib.Analysis.VonNeumannAlgebra.Basic Mathlib.Combinatorics.SimpleGraph.LapMatrix Mathlib.Geometry.Euclidean.Angle.Oriented.Basic Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus Mathlib.LinearAlgebra.Matrix.LDL Mathlib.LinearAlgebra.Matrix.PosDef Mathlib.LinearAlgebra.Matrix.SchurComplement Mathlib.LinearAlgebra.Matrix.Spectrum Mathlib.MeasureTheory.Function.AEEqOfIntegral Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1 Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator Mathlib.MeasureTheory.Function.ConditionalExpectation.Real Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique Mathlib.MeasureTheory.Function.FactorsThrough Mathlib.MeasureTheory.Integral.FundThmCalculus Mathlib.MeasureTheory.Integral.IntegrationByParts Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts Mathlib.MeasureTheory.Integral.IntervalIntegral Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue Mathlib.MeasureTheory.VectorMeasure.Decomposition.RadonNikodym Mathlib.MeasureTheory.VectorMeasure.WithDensity Mathlib.Probability.BorelCantelli Mathlib.Probability.CDF Mathlib.Probability.CondVar Mathlib.Probability.ConditionalExpectation Mathlib.Probability.Distributions.Uniform Mathlib.Probability.IdentDistrib Mathlib.Probability.Independence.Conditional Mathlib.Probability.Independence.ZeroOne Mathlib.Probability.Kernel.CompProdEqIff Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous Mathlib.Probability.Kernel.CondDistrib Mathlib.Probability.Kernel.Condexp Mathlib.Probability.Kernel.Disintegration.CDFToKernel Mathlib.Probability.Kernel.Disintegration.CondCDF Mathlib.Probability.Kernel.Disintegration.Density Mathlib.Probability.Kernel.Disintegration.Integral Mathlib.Probability.Kernel.Disintegration.StandardBorel Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Probability.Kernel.IonescuTulcea.Traj Mathlib.Probability.Kernel.Posterior Mathlib.Probability.Kernel.RadonNikodym Mathlib.Probability.Martingale.Basic Mathlib.Probability.Martingale.BorelCantelli Mathlib.Probability.Martingale.Centering Mathlib.Probability.Martingale.Convergence Mathlib.Probability.Martingale.OptionalSampling Mathlib.Probability.Martingale.OptionalStopping Mathlib.Probability.Martingale.Upcrossing Mathlib.Probability.Moments.Basic Mathlib.Probability.Moments.CovarianceBilin Mathlib.Probability.Moments.Covariance Mathlib.Probability.Moments.Variance Mathlib.Probability.Notation Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration Mathlib.Probability.Process.HittingTime Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Process.Stopping Mathlib.Probability.ProductMeasure Mathlib.Probability.StrongLaw Mathlib.Probability.Variance |
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190 filesMathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.CStarAlgebra.CStarMatrix Mathlib.Analysis.CStarAlgebra.CompletelyPositiveMap Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order Mathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Analysis.CStarAlgebra.Hom Mathlib.Analysis.CStarAlgebra.Module.Constructions Mathlib.Analysis.CStarAlgebra.Module.Defs Mathlib.Analysis.CStarAlgebra.PositiveLinearMap Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart Mathlib.Analysis.CStarAlgebra.Spectrum Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts Mathlib.Analysis.Calculus.Rademacher Mathlib.Analysis.Complex.AbsMax Mathlib.Analysis.Complex.CauchyIntegral Mathlib.Analysis.Complex.Hadamard Mathlib.Analysis.Complex.Liouville Mathlib.Analysis.Complex.LocallyUniformLimit Mathlib.Analysis.Complex.OpenMapping Mathlib.Analysis.Complex.Periodic Mathlib.Analysis.Complex.PhragmenLindelof Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Analysis.Complex.Positivity Mathlib.Analysis.Complex.RemovableSingularity Mathlib.Analysis.Complex.Schwarz Mathlib.Analysis.Complex.TaylorSeries Mathlib.Analysis.Complex.UpperHalfPlane.Exp Mathlib.Analysis.Complex.UpperHalfPlane.Manifold Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction Mathlib.Analysis.Complex.ValueDistribution.ProximityFunction Mathlib.Analysis.Convex.Integral Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Analysis.Fourier.AddCircleMulti Mathlib.Analysis.Fourier.AddCircle Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.Analysis.Fourier.Inversion Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.Analysis.MellinInversion Mathlib.Analysis.MellinTransform Mathlib.Analysis.Meromorphic.Gamma Mathlib.Analysis.Normed.Algebra.Basic Mathlib.Analysis.Normed.Algebra.Spectrum Mathlib.Analysis.NormedSpace.MultipliableUniformlyOn Mathlib.Analysis.ODE.PicardLindelof Mathlib.Analysis.SpecialFunctions.Complex.Analytic Mathlib.Analysis.SpecialFunctions.Complex.Arctan Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.Analysis.SpecialFunctions.Complex.LogBounds Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Isometric Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.Analysis.SpecialFunctions.Gamma.Beta Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup Mathlib.Analysis.SpecialFunctions.Gamma.Deligne Mathlib.Analysis.SpecialFunctions.Gamma.Deriv Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.Analysis.SpecialFunctions.ImproperIntegrals Mathlib.Analysis.SpecialFunctions.Integrals Mathlib.Analysis.SpecialFunctions.JapaneseBracket Mathlib.Analysis.SpecialFunctions.Log.Summable Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral Mathlib.Analysis.SpecialFunctions.NonIntegrable Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Analysis.SpecialFunctions.Stirling Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd Mathlib.Data.Real.Pi.Irrational Mathlib.Data.Real.Pi.Leibniz Mathlib.Data.Real.Pi.Wallis Mathlib.Geometry.Euclidean.Angle.Oriented.Affine Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle Mathlib.Geometry.Euclidean.Angle.Sphere Mathlib.Geometry.Euclidean.Sphere.Ptolemy Mathlib.Geometry.Euclidean.Triangle Mathlib.Geometry.Manifold.Complex Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique Mathlib.Geometry.Manifold.IntegralCurve.UniformTime Mathlib.InformationTheory.KullbackLeibler.Basic Mathlib.InformationTheory.KullbackLeibler.KLFun Mathlib.MeasureTheory.Constructions.HaarToSphere Mathlib.MeasureTheory.Integral.CircleAverage Mathlib.MeasureTheory.Integral.CircleIntegral Mathlib.MeasureTheory.Integral.CircleTransform Mathlib.MeasureTheory.Integral.ExpDecay Mathlib.MeasureTheory.Integral.Gamma Mathlib.MeasureTheory.Integral.IntegralEqImproper Mathlib.MeasureTheory.Integral.PeakFunction Mathlib.MeasureTheory.Integral.TorusIntegral Mathlib.MeasureTheory.Measure.CharacteristicFunction Mathlib.MeasureTheory.Measure.Decomposition.IntegralRNDeriv Mathlib.MeasureTheory.Measure.FiniteMeasureExt Mathlib.MeasureTheory.Measure.IntegralCharFun Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls Mathlib.NumberTheory.AbelSummation Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.Harmonic.Bounds Mathlib.NumberTheory.Harmonic.GammaDeriv Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.NumberTheory.LSeries.Deriv Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.NumberTheory.LSeries.MellinEqDirichlet Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.Positivity Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.LSeries.SumCoeff Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.ModularForms.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ModularForms.LevelOne Mathlib.NumberTheory.ModularForms.QExpansion Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.CMField Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal Mathlib.NumberTheory.NumberField.InfinitePlace.Basic Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart Mathlib.NumberTheory.ZetaValues Mathlib.Probability.Distributions.Exponential Mathlib.Probability.Distributions.Gamma Mathlib.Probability.Distributions.Gaussian.Basic Mathlib.Probability.Distributions.Gaussian.Real Mathlib.Probability.Distributions.Gaussian Mathlib.Probability.Distributions.Pareto Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.MGFAnalytic Mathlib.Probability.Moments.SubGaussian Mathlib.Probability.Moments.Tilted Mathlib.RingTheory.Polynomial.Selmer Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic |
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Mathlib.Analysis.LocallyConvex.Bipolar (new file) |
1876 |
Declarations diff
+ Bipolar
+ dualEmbedding_isSurjective
+ dualEquiv
+ strictEquiv2
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for script/declarations_diff.sh contains some details about this script.
No changes to technical debt.
You can run this locally as
./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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…losed and absolutely convex (#21002) Show that the absolute polar is weak*-closed and absolutely convex. Via `closedAbsConvexHull_min` this establishes the easy direction of the Bipolar Theorem #20843 Co-authored-by: Christopher Hoskin <[email protected]>
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…losed and absolutely convex (#21002) Show that the absolute polar is weak*-closed and absolutely convex. Via `closedAbsConvexHull_min` this establishes the easy direction of the Bipolar Theorem #20843 Co-authored-by: Christopher Hoskin <[email protected]>
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This PR has been migrated to a fork-based workflow: #26345 |
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WiP: The Bipolar Theorem
Following Conway, Chapter V. 1.8.