Theorems · Theorem · measure theory

MeasureTheory.addContent_biUnion_le

∀ {α : Type u_1} {C : Set (Set α)} {G : Type u_2} [inst : AddCommMonoid G] {m : MeasureTheory.AddContent G C}
  [inst_1 : PartialOrder G] [CanonicallyOrderedAdd G] {ι : Type u_3},
  MeasureTheory.IsSetRing C → ∀ {s : ι → Set α} {S : Finset ι}, (∀ n ∈ S, s n ∈ C) → m (⋃ i ∈ S, s i) ≤ ∑ i ∈ S, m (s i)

Defined in

Mathlib.MeasureTheory.Measure.AddContent

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderCanonicallyOrderedAdd