`BookProof.ChapterU.born_conditioning` (Ψ : X → ℂ) (μ : Measure X) (E : Set X) (hE : MeasurableSet E) (hpos : bornMeasure Ψ μ E ≠ 0) (_hfin : bornMeasure Ψ μ E ≠ ∞) : bornMeasure (

Proved

BookProof.ChapterU.born_conditioning

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterU.

BookProof.ChapterU.born_conditioning (Ψ : X → ℂ) (μ : Measure X) (E : Set X) (hE : MeasurableSet E) (hpos : bornMeasure Ψ μ E ≠ 0) (_hfin : bornMeasure Ψ μ E ≠ ∞) : bornMeasure (conditionedState Ψ μ E) μ = (bornMeasure Ψ μ)[|E]

Formalization note: Lean 4 identifier BookProof.ChapterU.born_conditioning.

Preamble

-- Generated from ChapterU.lean — theorem BookProof.ChapterU.born_conditioning
import Mathlib
import Definitions.Def_ChapterU
import Definitions.Def_ChapterBornMeasure
open BookProof.ChapterBornMeasure
open BookProof.ChapterU


open MeasureTheory
open scoped ENNReal ProbabilityTheory TensorProduct

variable {X : Type*} [MeasurableSpace X]

Formal statement

theorem BookProof.ChapterU.born_conditioning (Ψ : X → ℂ) (μ : Measure X) (E : Set X)
    (hE : MeasurableSet E) (hpos : bornMeasure Ψ μ E ≠ 0)
    (_hfin : bornMeasure Ψ μ E ≠ ∞) :
    bornMeasure (conditionedState Ψ μ E) μ = (bornMeasure Ψ μ)[|E] := by sorry

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