Theorems · Theorem · measure theory
MeasureTheory.measure_eq_zero_of_trim_eq_zero
∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} (hm : m ≤ m0),
(μ.trim hm) s = 0 → μ s = 0- Defined in
- Mathlib.MeasureTheory.Measure.Trim
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · 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 and proof · cited by 9,879
- le_reflproof · cited by 2,061
- le_imp_le_of_le_of_leproof · cited by 576
- MeasureTheory.Measure.trimstatement and proof · cited by 286
- nonpos_iff_eq_zeroproof · cited by 100
- MeasureTheory.le_trimproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_eq_of_ae_eq_trimproof · cited by 15
- MeasureTheory.ae_le_of_ae_le_trimproof · cited by 6
- MeasureTheory.ae_of_ae_trimproof · cited by 5
- MeasureTheory.Submartingale.ae_tendsto_limitProcessproof · cited by 4
- MeasureTheory.measure_trim_toMeasurable_eq_zeroproof · cited by 0