Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_empty
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}, μ.restrict ∅ = 0- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.measure_emptyproof · cited by 169
- MeasureTheory.Measure.restrict_zero_setproof · cited by 3
Cited by24
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_of_leproof · cited by 83
- MeasureTheory.integrableOn_emptyproof · cited by 6
- MonotoneOn.memLp_isCompactproof · cited by 3
- MeasureTheory.integral_biUnion_finsetproof · cited by 3
- MeasureTheory.exists_isSigmaFiniteSet_measure_geproof · cited by 3
- stronglyMeasurableAt_botproof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- sum_mul_eq_sub_integral_mul₁proof · cited by 2
- MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioiproof · cited by 2
- MeasureTheory.Integrable.tendsto_ae_condExpproof · cited by 2
- MeasureTheory.lintegral_eq_lintegral_of_isPiSystemproof · cited by 1
- ProbabilityTheory.condExp_generateFrom_singletonproof · cited by 1