Theorems · Theorem · measure theory
StieltjesFunction.measure_Ico
∀ {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] (a b : R),
f.measure (Set.Ico a b) = ENNReal.ofReal (Function.leftLim (↑f) b - Function.leftLim (↑f) a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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 · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- zero_addproof · cited by 2,366
- Disjointproof · cited by 2,201
- BorelSpacestatement and proof · cited by 1,602
- le_rflproof · cited by 1,558
Cited by2
Results whose statement or proof uses this declaration.
- Real.volume_Icoproof · cited by 6
- StieltjesFunction.measure_Iciproof · cited by 1