Theorems · Theorem · measure theory
MeasureTheory.measure_mono
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [MeasureTheory.OuterMeasureClass F α] {μ : F}
{s t : Set α}, s ⊆ t → μ s ≤ μ t- Defined in
- Mathlib.MeasureTheory.OuterMeasure.Basic
- Cited by
- 338 results in Mathlib
- Foundations
- Depth 108 from the axioms, rests on 1,990 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ENNRealstatement and proof · cited by 9,879
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
- MeasureTheory.OuterMeasureClass.measure_monoproof · cited by 1
Cited by338
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_mono_nullproof · cited by 81
- MeasureTheory.Measure.restrict_le_selfproof · cited by 57
- MeasureTheory.measure_iUnion_leproof · cited by 39
- MeasureTheory.measure_lt_topproof · cited by 39
- MeasureTheory.Measure.prod_prodproof · cited by 38
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- MeasureTheory.lintegral_iSupproof · cited by 16
- MeasurableEmbedding.map_applyproof · cited by 16
- MeasureTheory.VectorMeasure.variation_restrictproof · cited by 14
- MeasureTheory.measure_sdiff_nullproof · cited by 13
- MeasureTheory.tendsto_measure_iInter_atTopproof · cited by 12
- MeasureTheory.prob_le_oneproof · cited by 11
Showing the 200 most cited of 338.