Theorems · Theorem · measure theory
StieltjesFunction.measure_Ioc
∀ {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.Ioc a b) = ENNReal.ofReal (↑f b - ↑f a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- BorelSpacestatement and proof · cited by 1,602
- OrderTopologystatement and proof · cited by 1,355
- Set.Iocstatement and proof · cited by 971
- ENNReal.ofRealstatement and proof · cited by 863
Cited by8
Results whose statement or proof uses this declaration.
- Real.volume_Iocproof · cited by 11
- StieltjesFunction.measure_Iccproof · cited by 8
- StieltjesFunction.measure_Iicproof · cited by 8
- StieltjesFunction.measure_singletonproof · cited by 6
- StieltjesFunction.measure_Iooproof · cited by 3
- StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTopproof · cited by 2
- StieltjesFunction.measure_Iic_of_tendsto_atBot_atBotproof · cited by 1
- StieltjesFunction.eq_of_measure_of_eqproof · cited by 0