`BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff` {E : Set X} (hE : MeasurableSet E) : pvmMeasure P ψ E = 0 ↔ P.p E ψ = 0

Proved

BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPvmMeasure.

BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff {E : Set X} (hE : MeasurableSet E) : pvmMeasure P ψ E = 0 ↔ P.p E ψ = 0

Formalization note: Lean 4 identifier BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff.

Preamble

-- Generated from ChapterPvmMeasure.lean — theorem BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff
import Mathlib
import Definitions.Def_ChapterPvmMeasure
open BookProof.ChapterPvmMeasure


open MeasureTheory
open scoped InnerProductSpace


variable {X : Type*} [MeasurableSpace X]
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]

variable (P : Pvm X H)
variable (P : Pvm X H) (ψ : H)

Formal statement

theorem BookProof.ChapterPvmMeasure.pvmMeasure_eq_zero_iff {E : Set X} (hE : MeasurableSet E) :
    pvmMeasure P ψ E = 0 ↔ P.p E ψ = 0 := by sorry

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