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Theorems · Theorem · measure theory

MeasureTheory.measure_ne_top_of_subset

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {s t : Set α}, t ⊆ s → μ s ≠ ⊤ → μ t ≠ ⊤
Defined in
Mathlib.MeasureTheory.Measure.MeasureSpaceDef
Cited by
15 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.measureReal_union_le · cited by 4MeasureTheory.measureReal…MeasureTheory.measureReal_sdiff · cited by 4MeasureTheory.measureReal…MeasureTheory.measure_inter_ne_top_of_right_ne_top · cited by 3MeasureTheory.measure_int…MeasureTheory.measureReal_inter_add_sdiff · cited by 2MeasureTheory.measureReal…MeasureTheory.measureReal_inter_add_sdiff₀ · cited by 2MeasureTheory.measureReal…MeasureTheory.measureReal_add_sdiff · cited by 2MeasureTheory.measureReal…VitaliFamily.measure_limRatioMeas_top · cited by 2VitaliFamily.measure_limR…exists_eq_interval_average_of_nullSingletonClass · cited by 2exists_eq_interval_averag…MeasureTheory.measureReal_sdiff_null' · cited by 2MeasureTheory.measureReal…VitaliFamily.null_of_frequently_le_of_frequently_ge · cited by 1VitaliFamily.null_of_freq…MeasureTheory.measure_inter_ne_top_of_left_ne_top · cited by 1MeasureTheory.measure_int…VitaliFamily.measure_limRatioMeas_zero · cited by 1VitaliFamily.measure_limR…MeasureTheory.nonempty_inter_of_measureReal_lt_add · cited by 1MeasureTheory.nonempty_in…MeasureTheory.measureReal_union_congr_of_subset · cited by 0MeasureTheory.measureReal…MeasureTheory.measureReal_symmDiff_eq · cited by 0MeasureTheory.measureReal…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topLT.lt.ne · cited by 872lt.neMeasureTheory.measure_lt_top_of_subset · cited by 3MeasureTheory.measure_lt_…MeasureTheory.measure_ne_top_…CITED BYCITES

Cites8

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

Cited by15

Results whose statement or proof uses this declaration.