Theorems · Theorem · measure theory
StieltjesFunction.measure_Iio
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R)
[inst_2 : OrderTopology R] [inst_3 : CompactIccSpace R] [inst_4 : MeasurableSpace R] [inst_5 : BorelSpace R]
[inst_6 : SecondCountableTopology R] [inst_7 : DenselyOrdered R] {l : ℝ},
Filter.Tendsto (↑f) Filter.atBot (nhds l) →
∀ (x : R), f.measure (Set.Iio x) = ENNReal.ofReal (Function.leftLim (↑f) x - l)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites35
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- BorelSpacestatement and proof · cited by 1,602
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