Theorems · Theorem · measure theory
MeasureTheory.sfinite_sum_of_countable
∀ {α : Type u_1} {ι : Type u_3} {m0 : MeasurableSpace α} [Countable ι] (m : ι → MeasureTheory.Measure α)
[∀ (n : ι), MeasureTheory.IsFiniteMeasure (m n)], MeasureTheory.SFinite (MeasureTheory.Measure.sum m)A countable sum of finite measures is s-finite. This lemma is superseded by the instance below.
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- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.rangeproof · cited by 4,705
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Countablestatement and proof · cited by 633
- MeasureTheory.SFinitestatement · cited by 449
- MeasureTheory.Measure.sumstatement · cited by 121
- emproof · cited by 115
- Function.extendproof · cited by 111
- Pi.zero_applyproof · cited by 70
- Function.Injective.extend_applyproof · cited by 57
- Function.extend_apply'proof · cited by 30
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