Theorems · Theorem · measure theory
MeasureTheory.measureReal_restrict_apply
∀ {α : Type u_1} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α},
MeasurableSet t → (μ.restrict s).real t = μ.real (t ∩ s)- Defined in
- Mathlib.MeasureTheory.Measure.Real
- Cited by
- 29 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.
Cites10
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
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- MeasureTheory.Measure.restrict_applyproof · cited by 159
Cited by29
Results whose statement or proof uses this declaration.
- MeasureTheory.measureReal_restrict_apply_univproof · cited by 6
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- MeasureTheory.setIntegral_indicatorConstLpproof · cited by 4
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae'proof · cited by 2
- ProbabilityTheory.condDistrib_ae_eq_condExpproof · cited by 2
- ContDiffBump.measure_closedBall_le_integralproof · cited by 2
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2
- exists_eq_const_mul_setIntegral_of_ae_nonnegproof · cited by 2
- integral_gaussian_sq_complexproof · cited by 2
- MeasureTheory.SimpleFunc.hasBoxIntegralproof · cited by 2