Prove2Me

Import context: Probability/MomentMeasure/Affine

Definition
KLSModular_FunctionalInequalities_Probability_MomentMeasure_Affine

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.Affine 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.Affine, FunctionalInequalities.Probability.MomentMeasure.Integrability, and FunctionalInequalities.Probability.MomentMeasure.Basic. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Group.LIntegral, Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace, and Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap.

Original module imports

import FunctionalInequalities.Analysis.Convex.Affine
import FunctionalInequalities.Probability.MomentMeasure.Integrability
import FunctionalInequalities.Probability.MomentMeasure.Basic
import Mathlib.MeasureTheory.Group.LIntegral
import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap

Module navigation

Direct project imports: Analysis/Convex/Affine, Probability/MomentMeasure/Integrability, Probability/MomentMeasure/Basic.

Theorems in source order:

Project result: The KLS conjecture.

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

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Convex_Affine
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_MomentMeasure_Integrability
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_MomentMeasure_Basic
import Mathlib.MeasureTheory.Group.LIntegral
import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Probability/MomentMeasure/Affine.lean#L1-L176 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Probability.MomentMeasure.Affine`, import-context bundle `KLSModular_FunctionalInequalities_Probability_MomentMeasure_Affine`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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