Prove2Me

Import context: Probability/MomentMeasure/Coercivity

Definition
KLSModular_FunctionalInequalities_Probability_MomentMeasure_Coercivity

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-contextprobability

This bundle retains the import context of the source module FunctionalInequalities.Probability.MomentMeasure.Coercivity in the modular KLS dependency graph. It adds no new mathematical declarations. Substantive statements and proofs are represented by separate theorem nodes.

Its direct project prerequisite modules are FunctionalInequalities.Analysis.Convex.AffineMaximum, FunctionalInequalities.Probability.ConvexSupport, FunctionalInequalities.Probability.MomentMeasure.ConjugateMass, and FunctionalInequalities.Probability.MomentMeasure.Affine. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Measure.Haar.NormedSpace and Mathlib.MeasureTheory.Integral.Lebesgue.Map.

Original module imports

import FunctionalInequalities.Analysis.Convex.AffineMaximum
import FunctionalInequalities.Probability.ConvexSupport
import FunctionalInequalities.Probability.MomentMeasure.ConjugateMass
import FunctionalInequalities.Probability.MomentMeasure.Affine
import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
import Mathlib.MeasureTheory.Integral.Lebesgue.Map

Module navigation

Direct project imports: Analysis/Convex/AffineMaximum, Probability/ConvexSupport, Probability/MomentMeasure/ConjugateMass, Probability/MomentMeasure/Affine.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Probability.MomentMeasure.Coercivity · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_AffineMaximum
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_ConvexSupport
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_MomentMeasure_ConjugateMass
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_MomentMeasure_Affine
import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
import Mathlib.MeasureTheory.Integral.Lebesgue.Map
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Probability/MomentMeasure/Coercivity.lean#L1-L325 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Probability.MomentMeasure.Coercivity`, import-context bundle `KLSModular_FunctionalInequalities_Probability_MomentMeasure_Coercivity`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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