Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.apply_mono
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : MeasureTheory.FiniteMeasure Ω) {s₁ s₂ : Set Ω}, s₁ ⊆ s₂ → μ s₁ ≤ μ s₂- Cited by
- 5 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NNRealstatement · cited by 4,310
- MeasureTheory.measure_ne_topproof · cited by 171
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.toMeasureproof · cited by 87
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.OuterMeasure.monoproof · cited by 36
- ENNReal.toNNReal_monoproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.ProbabilityMeasure.apply_monoproof · cited by 5
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- MeasureTheory.FiniteMeasure.apply_le_massproof · cited by 1
- MeasureTheory.FiniteMeasure.mono_nullproof · cited by 1
- MeasureTheory.FiniteMeasure.pos_monoproof · cited by 0