Theorems · Theorem · measure theory

MeasureTheory.setIntegral_eq_of_subset_of_forall_sdiff_eq_zero

∀ {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 → s ⊆ t → (∀ x ∈ t \ s, f x = 0) → ∫ (x : X) in t, f x ∂μ = ∫ (x : X) in s, f x ∂μ

If a function vanishes on t \ s with s ⊆ t, then its integrals on s and t coincide if t is measurable.

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

3 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace