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Theorems · Theorem · measure theory

MeasureTheory.Measure.measure_univ_eq_zero

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}, μ Set.univ = 0 ↔ μ = 0
Defined in
Mathlib.MeasureTheory.Measure.MeasureSpace
Cited by
26 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.

MeasureTheory.IsProbabilityMeasure.ne_zero · cited by 17IsProbabilityMeasure.ne_z…MeasureTheory.Measure.restrict_eq_zero · cited by 17Measure.restrict_eq_zeroMeasureTheory.Measure.measure_univ_ne_zero · cited by 11Measure.measure_univ_ne_z…MeasureTheory.eq_zero_or_isProbabilityMeasure · cited by 6MeasureTheory.eq_zero_or_…MeasureTheory.FiniteMeasure.mass_zero_iff · cited by 5FiniteMeasure.mass_zero_i…MeasureTheory.ae_eq_bot · cited by 4MeasureTheory.ae_eq_botMeasureTheory.measure_smul_average · cited by 4MeasureTheory.measure_smu…MeasureTheory.Measure.MutuallySingular.self_iff · cited by 4MutuallySingular.self_iffMeasureTheory.Measure.absolutelyContinuous_zero_iff · cited by 3Measure.absolutelyContinu…Ergodic.of_mem_extremePoints_measure_univ_eq · cited by 2Ergodic.of_mem_extremePoi…MeasureTheory.withDensity_eq_zero_iff · cited by 2MeasureTheory.withDensity…MeasureTheory.lintegral_strict_mono · cited by 1MeasureTheory.lintegral_s…ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zero · cited by 1Kernel.withDensity_rnDeri…MeasureTheory.absolutelyContinuous_of_isAddLeftInvariant · cited by 1MeasureTheory.absolutelyC…MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant · cited by 1MeasureTheory.absolutelyC…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.univ · cited by 3945Set.univMeasureTheory.measure_mono · cited by 338MeasureTheory.measure_monoSet.subset_univ · cited by 228Set.subset_univbot_unique · cited by 57bot_uniqueMeasure.measure_univ_eq_zeroCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.