`BookProof.ChapterProbabilityInterface.translated_event_probability` {X Y : Type*} [MeasurableSpace X] [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X) (s : Set Y) (hs : Measurable

Proved

BookProof.ChapterProbabilityInterface.translated_event_probability

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterProbabilityInterface.

BookProof.ChapterProbabilityInterface.translated_event_probability {X Y : Type*} [MeasurableSpace X] [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X) (s : Set Y) (hs : MeasurableSet s) : transportMeasure e μ s = μ (e ⁻¹' s)

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

Preamble

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


open MeasureTheory

Formal statement

theorem BookProof.ChapterProbabilityInterface.translated_event_probability {X Y : Type*} [MeasurableSpace X]
    [MeasurableSpace Y] (e : X ≃ᵐ Y) (μ : Measure X)
    (s : Set Y) (hs : MeasurableSet s) :
    transportMeasure e μ s = μ (e ⁻¹' s) := by sorry

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