Theorems · Theorem · measure theory

MeasureTheory.Measure.map_apply_of_aemeasurable

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {f : α → β}, AEMeasurable f μ → ∀ {s : Set β}, MeasurableSet s → (MeasureTheory.Measure.map f μ) s = μ (f ⁻¹' s)

We can evaluate the pushforward on measurable sets. For non-measurable sets, see MeasureTheory.Measure.le_map_apply and MeasurableEquiv.map_apply.

Defined in

Mathlib.MeasureTheory.Measure.Map

Cited by

36 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound