Theorems · Theorem · measure theory
StieltjesFunction.measure_singleton
∀ {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 : R),
f.measure {a} = ENNReal.ofReal (↑f a - Function.leftLim (↑f) a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites66
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 · 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 and proof · cited by 9,879
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- nhdsproof · cited by 5,554
- Bot.botproof · cited by 4,720
- Filter.Tendstoproof · cited by 3,814
Cited by6
Results whose statement or proof uses this declaration.
- StieltjesFunction.measure_Iccproof · cited by 8
- StieltjesFunction.measure_Iooproof · cited by 3
- StieltjesFunction.measure_Icoproof · cited by 2
- StieltjesFunction.measure_botSetproof · cited by 0
- StieltjesFunction.measure_Iioproof · cited by 0
- StieltjesFunction.measure_Ioiproof · cited by 0