Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_le

∀ {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} {m : MeasureTheory.Measure X},
  MeasurableSet s → (∀ (E : Set X), MeasurableSet E → E ⊆ s → ‖μ E‖ₑ ≤ m E) → μ.variation s ≤ m s

Defined in

Mathlib.MeasureTheory.VectorMeasure.Variation.Basic

Cited by

3 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddCommMonoidT2Space