Theorems · Theorem · measure theory
MeasureTheory.measure_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure μ] (s : Set α),
μ s < ⊤- Cited by
- 39 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- LE.le.trans_ltproof · cited by 795
- MeasureTheory.measure_monoproof · cited by 338
- Set.subset_univproof · cited by 228
- MeasureTheory.IsFiniteMeasure.measure_univ_lt_topproof · cited by 6
Cited by39
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_ne_topproof · cited by 171
- MeasureTheory.FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasureproof · cited by 11
- BoundedContinuousFunction.integrableproof · cited by 9
- MeasureTheory.Measure.lintegral_rnDeriv_lt_topproof · cited by 9
- ProbabilityTheory.Kernel.integrable_densityproof · cited by 6
- MeasureTheory.isFiniteMeasure_of_leproof · cited by 4
- MeasureTheory.exists_isSigmaFiniteSet_measure_geproof · cited by 3
- ProbabilityTheory.Kernel.integrable_densityProcessproof · cited by 3
- AddMonoidHom.measurePreservingproof · cited by 2
- ProbabilityTheory.condDistrib_ae_eq_condExpproof · cited by 2
- MeasureTheory.Integrable.tendsto_ae_condExpproof · cited by 2
- MeasureTheory.SimpleFunc.hasBoxIntegralproof · cited by 2