Theorems · Theorem · measure theory
MeasureTheory.preVariation.sum_le_preVariationFun_iUnion
∀ {X : Type u_1} [inst : MeasurableSpace X] (f : Set X → ENNReal) {s : ℕ → Set X},
(∀ (i : ℕ), MeasurableSet (s i)) →
Pairwise (Function.onFun Disjoint s) →
∑' (i : ℕ), MeasureTheory.preVariationFun f (s i) ≤ MeasureTheory.preVariationFun f (⋃ i, s i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Finset.sumproof · cited by 5,195
- NNRealproof · cited by 4,310
- MeasurableSetstatement and proof · cited by 3,075
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Set.iUnionstatement and proof · cited by 2,483
- Disjointstatement and proof · cited by 2,201
- SummationFilter.unconditionalstatement · cited by 2,068
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.preVariation.iUnionproof · cited by 0