`BookProof.ChapterProbabilityInterface.transportMeasure_isProbability` {X Y : Type*} [MeasurableSpace X] [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X) [IsProbabilityMeasure μ] :

Proved

BookProof.ChapterProbabilityInterface.transportMeasure_isProbability

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterProbabilityInterface.

BookProof.ChapterProbabilityInterface.transportMeasure_isProbability {X Y : Type*} [MeasurableSpace X] [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X) [IsProbabilityMeasure μ] : IsProbabilityMeasure (transportMeasure e μ)

Formalization note: Lean 4 identifier BookProof.ChapterProbabilityInterface.transportMeasure_isProbability.

Preamble

-- Generated from ChapterProbabilityInterface.lean — theorem BookProof.ChapterProbabilityInterface.transportMeasure_isProbability
import Mathlib
import Definitions.Def_ChapterProbabilityInterface
open BookProof.ChapterProbabilityInterface


open MeasureTheory

Formal statement

theorem BookProof.ChapterProbabilityInterface.transportMeasure_isProbability {X Y : Type*} [MeasurableSpace X]
    [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X)
    [IsProbabilityMeasure μ] : IsProbabilityMeasure (transportMeasure e μ) := by sorry

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