`BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul` [IsFiniteMeasure nu] (hne : nu Set.univ ≠ 0) : IsProbabilityMeasure ((nu Set.univ)⁻¹ • nu)

Proved

BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpScaleMeasure.

BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul [IsFiniteMeasure nu] (hne : nu Set.univ ≠ 0) : IsProbabilityMeasure ((nu Set.univ)⁻¹ • nu)

Formalization note: Lean 4 identifier BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul.

Preamble

-- Generated from ChapterLpScaleMeasure.lean — theorem BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterLpScaleMeasure
open BookProof.ChapterLpScaleMeasure


noncomputable section

open MeasureTheory ENNReal


open BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] {nu : Measure α} {c : ENNReal}

Formal statement

theorem BookProof.ChapterLpScaleMeasure.isProbabilityMeasure_inv_smul [IsFiniteMeasure nu] (hne : nu Set.univ ≠ 0) :
    IsProbabilityMeasure ((nu Set.univ)⁻¹ • nu) := by sorry

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