Theorems · Theorem · measure theory
StieltjesFunction.length_Ioc
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R) (a b : R),
f.length (Set.Ioc a b) = ENNReal.ofReal (↑f b - ↑f a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement and proof · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- NNRealproof · cited by 4,310
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Set.Iocstatement and proof · cited by 971
- ENNReal.ofRealstatement and proof · cited by 863
- le_imp_le_of_le_of_leproof · cited by 576
- zero_leproof · cited by 382
- le_or_gtproof · cited by 269
Cited by2
Results whose statement or proof uses this declaration.
- StieltjesFunction.outer_Iocproof · cited by 2
- StieltjesFunction.measurableSet_Ioiproof · cited by 1