Theorems · Theorem · measure theory
ENNReal.tsum_iUnion_le
∀ {α : Type u_1} {ι : Type u_4} [inst : Fintype ι] (f : α → ENNReal) (t : ι → Set α),
∑' (x : ↑(⋃ i, t i)), f ↑x ≤ ∑ i, ∑' (x : ↑(t i)), f ↑x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- ENNRealstatement and proof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- Set.iUnionstatement and proof · cited by 2,483
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- tsum_fintypeproof · cited by 38
- ENNReal.tsum_iUnion_le_tsumproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.tsum_union_leproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1