Theorems · Theorem · measure theory
MeasureTheory.ProbabilityMeasure.apply_mono
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : MeasureTheory.ProbabilityMeasure Ω) {s₁ s₂ : Set Ω},
s₁ ⊆ s₂ → μ s₁ ≤ μ s₂- Cited by
- 5 results in Mathlib
- Foundations
- Depth 178 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.
Cites8
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 and proof · cited by 4,310
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- MeasureTheory.ProbabilityMeasure.toFiniteMeasureproof · cited by 26
- MeasureTheory.FiniteMeasure.apply_monoproof · cited by 5
- MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFnproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- IsPiSystem.tendsto_probabilityMeasure_of_tendsto_of_memproof · cited by 2
- MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closureproof · cited by 1
- isCompact_closure_of_isTightMeasureSetproof · cited by 1
- MeasureTheory.ProbabilityMeasure.apply_le_oneproof · cited by 1
- MeasureTheory.isTightMeasureSet_of_isCompact_closureproof · cited by 0