Theorems · Theorem · measure theory
MeasureTheory.self_mem_ae_restrict
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasurableSet s → s ∈ MeasureTheory.ae (μ.restrict s)- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 13 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.
- 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.univproof · cited by 3,945
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Set.univ_interproof · cited by 258
- Set.Subset.rflproof · cited by 255
- Filter.univ_memproof · cited by 96
- MeasureTheory.ae_restrict_eqproof · cited by 11
Cited by13
Results whose statement or proof uses this declaration.
- ContinuousOn.aestronglyMeasurableproof · cited by 21
- Real.Gamma_pos_of_posproof · cited by 17
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
- MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mulproof · cited by 1
- MeasureTheory.AEContinuous.hasBoxIntegralproof · cited by 1
- Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gammaproof · cited by 1
- ContinuousOn.aestronglyMeasurable_of_isSeparableproof · cited by 1
- intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Iccproof · cited by 1
- enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Iccproof · cited by 1
- enorm_sub_le_lintegral_deriv_of_contDiffOn_Iccproof · cited by 1