Theorems · Theorem · measure theory

MeasurableEquiv.map_apply

∀ {α : Type u_1} {β : Type u_2} {x : MeasurableSpace α} [inst : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  (f : α ≃ᵐ β) (s : Set β), (MeasureTheory.Measure.map (⇑f) μ) s = μ (⇑f ⁻¹' s)

If we map a measure along a measurable equivalence, we can compute the measure on all sets (not just the measurable ones).

Defined in

Mathlib.MeasureTheory.Measure.Map

Cited by

26 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace