Prove2Me

Import context: Analysis/BakryEmery/IntegrationByParts/ConvexHessian

Definition
KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_ConvexHessian

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

analysisfunctional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context

This bundle retains the import context of the source module FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.ConvexHessian 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.BakryEmery.IntegrationByParts.Basic, FunctionalInequalities.Analysis.BakryEmery.Bochner.Basic, FunctionalInequalities.Analysis.Cutoff.SmoothBall, and FunctionalInequalities.Analysis.Cutoff.Integrability. It also directly imports the external prerequisite module Mathlib.MeasureTheory.Function.L2Space.

Original module imports

import FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.Basic
import FunctionalInequalities.Analysis.BakryEmery.Bochner.Basic
import FunctionalInequalities.Analysis.Cutoff.SmoothBall
import FunctionalInequalities.Analysis.Cutoff.Integrability
import Mathlib.MeasureTheory.Function.L2Space

Module navigation

Direct project imports: Analysis/BakryEmery/IntegrationByParts/Basic, Analysis/BakryEmery/Bochner/Basic, Analysis/Cutoff/SmoothBall, Analysis/Cutoff/Integrability.

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.ConvexHessian · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Bochner_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Cutoff_SmoothBall
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Cutoff_Integrability
import Mathlib.MeasureTheory.Function.L2Space
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Analysis/BakryEmery/IntegrationByParts/ConvexHessian.lean#L1-L234 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Analysis.BakryEmery.IntegrationByParts.ConvexHessian`, import-context bundle `KLSModular_FunctionalInequalities_Analysis_BakryEmery_IntegrationByParts_ConvexHessian`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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