Theorems · Theorem · measure theory

MeasureTheory.lintegral_indicator_const_comp

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {f : α → β} {s : Set β},
  Measurable f → MeasurableSet s → ∀ (c : ENNReal), ∫⁻ (a : α), s.indicator (fun x => c) (f a) ∂μ = c * μ (f ⁻¹' s)

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Map

Cited by

3 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace