Theorems · Theorem · measure theory
StieltjesFunction.measure_univ
∀ {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] [Nonempty R] {l u : ℝ},
Filter.Tendsto (↑f) Filter.atBot (nhds l) →
Filter.Tendsto (↑f) Filter.atTop (nhds u) → f.measure Set.univ = ENNReal.ofReal (u - l)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 · 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 · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement and proof · cited by 5,554
- Set.univstatement · cited by 3,945
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
Cited by5
Results whose statement or proof uses this declaration.
- StieltjesFunction.isFiniteMeasureproof · cited by 1
- ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univproof · cited by 1
- StieltjesFunction.isProbabilityMeasureproof · cited by 1
- ProbabilityTheory.cdf_measure_stieltjesFunctionproof · cited by 0
- ProbabilityTheory.measure_condCDF_univproof · cited by 0