Theorems · Theorem · measure theory

MeasureTheory.setIntegral_indicator

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {f : X → E} {s t : Set X} {μ : MeasureTheory.Measure X},
  MeasurableSet t → ∫ (x : X) in s, t.indicator f x ∂μ = ∫ (x : X) in s ∩ t, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

3 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace