Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_congr_set
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α},
s =ᵐ[μ] t → μ.restrict s = μ.restrict t- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasureTheory.aestatement and proof · cited by 2,352
- le_antisymmproof · cited by 2,068
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Filter.EventuallyEq.symmproof · cited by 408
- Filter.EventuallyEq.leproof · cited by 46
- MeasureTheory.Measure.restrict_mono_aeproof · cited by 3
Cited by43
Results whose statement or proof uses this declaration.
- MeasureTheory.setIntegral_congr_setproof · cited by 22
- MeasureTheory.setLIntegral_congrproof · cited by 11
- MeasureTheory.Measure.restrict_eq_self_of_ae_memproof · cited by 10
- MeasureTheory.restrict_Ioo_eq_restrict_Iocproof · cited by 7
- MeasureTheory.Measure.restrict_apply₀'proof · cited by 7
- MeasureTheory.restrict_Ioo_eq_restrict_Iccproof · cited by 6
- MeasureTheory.IsFundamentalDomain.sum_restrict_of_acproof · cited by 4
- MeasureTheory.IsAddFundamentalDomain.sum_restrict_of_acproof · cited by 4
- MeasureTheory.lintegral_indicator₀proof · cited by 4
- intervalIntegral.integral_comp_mul_rightproof · cited by 3
- aemeasurable_indicator_iff₀proof · cited by 2
- MeasureTheory.ae_restrict_of_ae_eq_of_ae_restrictproof · cited by 2