Theorems · Theorem · measure theory
MeasureTheory.restrict_trim
∀ {α : Type u_1} {m m0 : MeasurableSpace α} {s : Set α} (hm : m ≤ m0) (μ : MeasureTheory.Measure α),
MeasurableSet s → (μ.trim hm).restrict s = (μ.restrict s).trim hm- Defined in
- Mathlib.MeasureTheory.Measure.Trim
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- ENNRealproof · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.trimstatement and proof · cited by 286
- MeasurableSet.interproof · cited by 167
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.trim_measurableSet_eqproof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.condExp_restrict_ae_eq_restrictproof · cited by 8
- MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'proof · cited by 5
- MeasureTheory.setIntegral_trimproof · cited by 5
- MeasureTheory.condExp_ae_eq_restrict_zeroproof · cited by 2
- MeasureTheory.setLIntegral_trim_aeproof · cited by 2
- MeasureTheory.trim_withDensityproof · cited by 0