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Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.measurable

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {x : MeasurableSpace α} [inst : TopologicalSpace β]
  [TopologicalSpace.PseudoMetrizableSpace β] [inst_2 : MeasurableSpace β] [BorelSpace β],
  MeasureTheory.StronglyMeasurable f → Measurable f

A strongly measurable function is measurable.

Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
Cited by
74 results in Mathlib
Foundations
Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceMeasurableSpaceBorelSpace

Around this declaration

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

MeasureTheory.AEStronglyMeasurable.aemeasurable · cited by 73AEStronglyMeasurable.aeme…MeasureTheory.StronglyMeasurable.enorm · cited by 19StronglyMeasurable.enormstronglyMeasurable_iff_measurable_separable · cited by 13stronglyMeasurable_iff_me…stronglyMeasurable_of_tendsto · cited by 12stronglyMeasurable_of_ten…MeasureTheory.StronglyMeasurable.measurableSet_le · cited by 9StronglyMeasurable.measur…MeasureTheory.integral_trim · cited by 6MeasureTheory.integral_tr…MeasureTheory.StronglyAdapted.adapted · cited by 5StronglyAdapted.adaptedMeasureTheory.integral_mono_measure · cited by 5MeasureTheory.integral_mo…MeasureTheory.AEStronglyMeasurable.measurable_mk · cited by 4AEStronglyMeasurable.meas…MeasureTheory.Submartingale.ae_tendsto_limitProcess · cited by 4Submartingale.ae_tendsto_…MeasureTheory.integral_dirac' · cited by 4MeasureTheory.integral_di…MeasureTheory.tendstoInMeasure_of_tendsto_ae · cited by 4MeasureTheory.tendstoInMe…MeasureTheory.StronglyMeasurable.measurableSet_eq_fun · cited by 3StronglyMeasurable.measur…MeasureTheory.StronglyMeasurable.measurableSet_exists_tendsto · cited by 3StronglyMeasurable.measur…MeasureTheory.memLp_add_of_disjoint · cited by 3MeasureTheory.memLp_add_o…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceBorelSpace · cited by 1602BorelSpaceMeasurable · cited by 1499MeasurableMeasureTheory.StronglyMeasurable · cited by 363MeasureTheory.StronglyMea…TopologicalSpace.PseudoMetrizableSpace · cited by 245TopologicalSpace.PseudoMe…tendsto_pi_nhds · cited by 58tendsto_pi_nhdsMeasureTheory.StronglyMeasurable.approx · cited by 40StronglyMeasurable.approxMeasureTheory.StronglyMeasurable.tendsto_approx · cited by 36StronglyMeasurable.tendst…MeasureTheory.SimpleFunc.measurable · cited by 20SimpleFunc.measurablemeasurable_of_tendsto_metrizable · cited by 6measurable_of_tendsto_met…StronglyMeasurable.measurableCITED BYCITES

Cites11

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Cited by74

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