Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_le
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasureTheory.ae (μ.restrict s) ≤ MeasureTheory.ae μ- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 5 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filterstatement · cited by 8,121
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.Measure.restrict_le_selfproof · cited by 57
- MeasureTheory.ae_monoproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.setIntegral_condExp_le_of_ae_nonnegproof · cited by 1
- MeasureTheory.setLAverage_le_essSupproof · cited by 1
- MeasureTheory.setIntegral_norm_condExp_rpow_leproof · cited by 1
- ProbabilityTheory.condExpKernel_singleton_ae_eq_condproof · cited by 0
- MeasureTheory.IntegrableAtFilter.congr'_enormproof · cited by 0