Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_apply

∀ {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),
  μ.variation s = (MeasureTheory.preVariation (fun x => ‖μ x‖ₑ) ⋯ ⋯) s

Defined in

Mathlib.MeasureTheory.VectorMeasure.Variation.Basic

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddCommMonoidT2Space