Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_le_restrict_iff

∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
  [inst_2 : PartialOrder M] (v w : MeasureTheory.VectorMeasure α M) {i : Set α},
  MeasurableSet i → (v.restrict i ≤ w.restrict i ↔ ∀ ⦃j : Set α⦄, MeasurableSet j → j ⊆ i → v j ≤ w j)

Defined in

Mathlib.MeasureTheory.VectorMeasure.Basic

Cited by

12 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommMonoidPartialOrder