Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_toMeasurable
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
μ s ≠ ⊤ → μ.restrict (MeasureTheory.toMeasurable μ s) = μ.restrict s- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 197 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.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 · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.univ_interproof · cited by 258
- Set.subset_univproof · cited by 228
- MeasurableSet.univproof · cited by 178
- MeasureTheory.toMeasurablestatement and proof · cited by 77
- MeasureTheory.Measure.restrict_inter_toMeasurableproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_nonneg_of_forall_setIntegral_nonnegproof · cited by 3
- MeasureTheory.ae_le_of_forall_setLIntegral_le_of_sigmaFinite₀proof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.restrictproof · cited by 1
- ProbabilityTheory.cond_toMeasurable_eqproof · cited by 1
- MeasureTheory.pdf.IsUniform.hasPDFproof · cited by 1
- Convex.average_mem_interior_of_setproof · cited by 0