Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.setIntegral_eq_zero_of_ae_eq_zero

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedAddCommGroup G] {μ : MeasureTheory.VectorMeasure X F} {f : X → E}
  {t : Set X} [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace ℝ G] {B : E →L[ℝ] F →L[ℝ] G},
  (∀ᵐ (x : X) ∂μ.variation, x ∈ t → f x = 0) → ∫ᵛ (x : X) in t, f x ∂[B; μ] = 0

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

1 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace