Theorems · Theorem · measure theory
MeasureTheory.Measure.sum_apply_of_countable
∀ {α : Type u_1} {ι : Type u_5} {m0 : MeasurableSpace α} [Countable ι] (f : ι → MeasureTheory.Measure α) (s : Set α),
(MeasureTheory.Measure.sum f) s = ∑' (i : ι), (f i) s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetproof · cited by 3,075
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- le_antisymmproof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Countablestatement and proof · cited by 633
- MeasureTheory.measure_monoproof · cited by 338
- MeasureTheory.Measure.sumstatement · cited by 121
Cited by4
Results whose statement or proof uses this declaration.
- measurable_measure_prodMk_leftproof · cited by 20
- MeasureTheory.exists_isFiniteMeasure_absolutelyContinuousproof · cited by 4
- MeasureTheory.Measure.restrict_sum_of_countableproof · cited by 2
- MeasureTheory.Measure.sum_apply_eq_zeroproof · cited by 1