Theorems · Theorem · measure theory

MeasureTheory.Measure.restrict_mono

∀ {α : Type u_2} {_m0 : MeasurableSpace α} ⦃s s' : Set α⦄,
  s ⊆ s' → ∀ ⦃μ ν : MeasureTheory.Measure α⦄, μ ≤ ν → μ.restrict s ≤ ν.restrict s'

Restriction of a measure to a subset is monotone both in set and in measure.

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

33 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound