Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_apply_eq_zero

∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
  [inst_2 : T2Space V] {μ : MeasureTheory.VectorMeasure X V} {s : Set X},
  MeasurableSet s → (μ.variation s = 0 ↔ ∀ t ⊆ s, MeasurableSet t → μ t = 0)

Defined in

Mathlib.MeasureTheory.VectorMeasure.Variation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddCommMonoidT2Space