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Theorems · Definition · measure theory

MeasureTheory.Measure.FiniteAtFilter

{α : Type u_1} → {_m0 : MeasurableSpace α} → MeasureTheory.Measure α → Filter α → Prop

A measure is called finite at filter f if it is finite at some set s ∈ f. Equivalently, it is eventually finite at s in f.small_sets.

Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.Finite
Cited by
35 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.Measure.finiteAt_nhds · cited by 10Measure.finiteAt_nhdsMeasureTheory.Measure.FiniteAtFilter.filter_mono · cited by 6FiniteAtFilter.filter_monoMeasureTheory.Measure.FiniteAtFilter.eventually · cited by 4FiniteAtFilter.eventuallyintervalIntegral.FTCFilter.finiteAt_inner · cited by 4FTCFilter.finiteAt_innerMeasureTheory.Measure.finiteAt_nhdsWithin · cited by 3Measure.finiteAt_nhdsWith…Filter.Tendsto.integral_sub_linear_isLittleO_ae · cited by 3Tendsto.integral_sub_line…MeasureTheory.Measure.FiniteAtFilter.exists_mem_basis · cited by 3FiniteAtFilter.exists_mem…Filter.Tendsto.integrableAtFilter · cited by 2Tendsto.integrableAtFilterMeasureTheory.Measure.FiniteAtFilter.inf_ae_iff · cited by 2FiniteAtFilter.inf_ae_iffintervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae' · cited by 2intervalIntegral.measure_…MeasureTheory.Measure.FiniteAtFilter.inf_of_left · cited by 2FiniteAtFilter.inf_of_leftintervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' · cited by 2intervalIntegral.measure_…MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter · cited by 2FiniteAtFilter.integrable…MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae · cited by 2FiniteAtFilter.integrable…MeasureTheory.Measure.FiniteAtFilter.measure_mono · cited by 2FiniteAtFilter.measure_mo…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureTop.top · cited by 9680Top.topFilter · cited by 8121FilterMeasure.FiniteAtFilterCITED BYCITES

Cites6

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Cited by37

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