Theorems · Theorem · measure theory
MeasureTheory.Measure.sum_apply
∀ {α : Type u_1} {ι : Type u_5} {m0 : MeasurableSpace α} (f : ι → MeasureTheory.Measure α) {s : Set α},
MeasurableSet s → (MeasureTheory.Measure.sum f) s = ∑' (i : ι), (f i) s- Cited by
- 50 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- MeasurableSetstatement and proof · cited by 3,075
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- MeasureTheory.Measure.sumstatement · cited by 121
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.toMeasure_applyproof · cited by 10
- MeasureTheory.OuterMeasure.sumproof · cited by 5
Cited by50
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.prod_swapproof · cited by 14
- MeasureTheory.Measure.le_sumproof · cited by 9
- MeasureTheory.Measure.map_sumproof · cited by 9
- ProbabilityTheory.Kernel.sum_apply'proof · cited by 6
- MeasureTheory.Measure.restrict_iUnion_aeproof · cited by 5
- MeasureTheory.Measure.restrict_iUnion_leproof · cited by 5
- MeasureTheory.exists_isFiniteMeasure_absolutelyContinuousproof · cited by 4
- MeasureTheory.Measure.sum_apply_of_countableproof · cited by 4
- MeasureTheory.Measure.count_applyproof · cited by 3
- MeasureTheory.Measure.sum_fintypeproof · cited by 3
- MeasureTheory.Measure.prod_sum_leftproof · cited by 3
- MeasureTheory.Measure.prod_sum_rightproof · cited by 3