Theorems · Theorem · measure theory
MeasureTheory.OuterMeasure.isCaratheodory_iUnion_of_disjoint
∀ {α : Type u} (m : MeasureTheory.OuterMeasure α) {s : ℕ → Set α},
(∀ (i : ℕ), m.IsCaratheodory (s i)) → Pairwise (Function.onFun Disjoint s) → m.IsCaratheodory (⋃ i, s i)Use isCaratheodory_iUnion instead, which does not require the disjoint assumption.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- ENNRealproof · cited by 9,879
- Set.iUnionstatement and proof · cited by 2,483
- iSupproof · cited by 2,415
- Disjointstatement and proof · cited by 2,201
- SummationFilter.unconditionalproof · cited by 2,068
- le_reflproof · cited by 2,061
- tsumproof · cited by 1,148
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- Function.onFunstatement and proof · cited by 570
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.isCaratheodory_iUnionproof · cited by 1