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feature(Analysis/LocallyConvex/Polar): Show that the polar is weak*-closed and absolutely convex #21002
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PR summary 89774b7a34Import changes exceeding 2%
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File | Base Count | Head Count | Change |
---|---|---|---|
Mathlib.Analysis.LocallyConvex.Polar | 1308 | 1368 | +60 (+4.59%) |
Mathlib.Analysis.Normed.Module.Dual | 1764 | 1768 | +4 (+0.23%) |
Import changes for all files
Files | Import difference |
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158 filesMathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.CStarAlgebra.CStarMatrix Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic 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.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.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.NormPow Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.Analysis.MellinInversion Mathlib.Analysis.MellinTransform Mathlib.Analysis.Normed.Algebra.Basic Mathlib.Analysis.Normed.Algebra.Spectrum 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.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.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.MeasureTheory.Constructions.HaarToSphere Mathlib.MeasureTheory.Decomposition.IntegralRNDeriv 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.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.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.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.Transcendental.Lindemann.Init.AnalyticalPart Mathlib.NumberTheory.ZetaValues Mathlib.Probability.Distributions.Exponential Mathlib.Probability.Distributions.Gamma Mathlib.Probability.Distributions.Gaussian Mathlib.Probability.Distributions.Pareto Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.MGFAnalytic Mathlib.RingTheory.Polynomial.Selmer Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic |
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69 filesMathlib.Analysis.CStarAlgebra.ContinuousLinearMap Mathlib.Analysis.CStarAlgebra.Matrix Mathlib.Analysis.Convex.Cone.Proper 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.Decomposition.RadonNikodym Mathlib.MeasureTheory.Decomposition.SignedLebesgue 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.Integral.FundThmCalculus Mathlib.MeasureTheory.Measure.LogLikelihoodRatio Mathlib.MeasureTheory.Measure.Tilted Mathlib.MeasureTheory.Measure.WithDensityFinite Mathlib.MeasureTheory.VectorMeasure.WithDensity Mathlib.Probability.BorelCantelli Mathlib.Probability.CDF Mathlib.Probability.CondVar Mathlib.Probability.ConditionalExpectation Mathlib.Probability.Density Mathlib.Probability.Distributions.Uniform Mathlib.Probability.IdentDistrib Mathlib.Probability.Independence.Conditional Mathlib.Probability.Independence.ZeroOne 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.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.Notation Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration Mathlib.Probability.Process.HittingTime Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Process.Stopping Mathlib.Probability.StrongLaw Mathlib.Probability.Variance |
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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 |
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Mathlib.Analysis.LocallyConvex.Polar |
60 |
Declarations diff
+ AbsConvex.iInter₂
+ Balanced.mulActionHom_preimage
+ balanced_closedBall_zero
+ closedBall_normSeminorm
+ polar_AbsConvex
+ polar_eq_biInter_preimage
+ polar_isClosed
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
relative
value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolute
value is therelative
value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
Oops - forgot to remove the |
Co-authored-by: Jireh Loreaux <[email protected]>
Co-authored-by: Jireh Loreaux <[email protected]>
Co-authored-by: Jireh Loreaux <[email protected]>
The import increase is unacceptably large. Can you try to find a better place with |
(N.B. I haven't used |
I think that's because in your branch you've edited the |
I'm not really getting how this is supposed to work. I removed
But |
I had another go, copying the lemma into |
Weirdly
I don't understand what's happening here? |
Show that the absolute polar is weak*-closed and absolutely convex.
Via
closedAbsConvexHull_min
this establishes the easy direction of the Bipolar Theorem #20843