Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_eq
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasurableSet s → MeasureTheory.ae (μ.restrict s) = MeasureTheory.ae μ ⊓ Filter.principal s- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 11 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.
Cites13
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
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- MeasurableSetstatement and proof · cited by 3,075
- Compl.complproof · cited by 2,925
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Filter.principalstatement · cited by 740
- Filter.extproof · cited by 60
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.self_mem_ae_restrictproof · cited by 13
- MeasureTheory.setIntegral_mono_onproof · cited by 11
- MeasureTheory.Measure.FiniteAtFilter.integrableAtFilterproof · cited by 2
- ENNReal.essSup_piecewiseproof · cited by 2
- Polynomial.Chebyshev.integrable_measureTproof · cited by 2
- intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_ltproof · cited by 2
- piecewise_ae_eq_restrictproof · cited by 2
- TorusIntegrable.function_integrableproof · cited by 2
- MeasureTheory.isTightMeasureSet_of_tendsto_charFunproof · cited by 1
- piecewise_ae_eq_restrict_complproof · cited by 1
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1