Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_map

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} [inst : MeasurableSpace β] {M : Type u_3}
  [inst_1 : AddCommMonoid M] [inst_2 : TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) {f : α → β},
  Measurable f → ∀ {s : Set β}, MeasurableSet s → (v.map f).restrict s = (v.restrict (f ⁻¹' s)).map f

Defined in

Mathlib.MeasureTheory.VectorMeasure.Basic

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddCommMonoidTopologicalSpace