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Theorems · Theorem · measure theory

MeasureTheory.Integrable.mono_measure

∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] {f : α → ε}, MeasureTheory.Integrable f ν → μ ≤ ν → MeasureTheory.Integrable f μ
Defined in
Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by
26 results in Mathlib
Foundations
Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceContinuousENorm

Around this declaration

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

MeasureTheory.IntegrableOn.mono · cited by 22IntegrableOn.monoMeasureTheory.Integrable.restrict · cited by 15Integrable.restrictMeasureTheory.IntegrableOn.union · cited by 8IntegrableOn.unionMeasureTheory.integral_mono_measure · cited by 5MeasureTheory.integral_mo…MeasureTheory.VectorMeasure.IntegrableOn.mono · cited by 4IntegrableOn.monoMeasureTheory.hasSum_integral_measure · cited by 4MeasureTheory.hasSum_inte…MeasureTheory.Integrable.comp_add_right · cited by 2Integrable.comp_add_rightMeasureTheory.IntegrableOn.mono_set_ae · cited by 2IntegrableOn.mono_set_aeMeasureTheory.Integrable.comp_neg · cited by 2Integrable.comp_negMeasureTheory.setToFun_of_le_map_of_stronglyMeasurable · cited by 2MeasureTheory.setToFun_of…MeasureTheory.integral_inter_add_sdiff₀ · cited by 2MeasureTheory.integral_in…MeasureTheory.Integrable.comp_add_left · cited by 2Integrable.comp_add_leftMeasureTheory.VectorMeasure.Integrable.add_vectorMeasure · cited by 2Integrable.add_vectorMeas…MeasureTheory.VectorMeasure.Integrable.neg_vectorMeasure · cited by 2Integrable.neg_vectorMeas…MeasureTheory.IntegrableOn.mono_measure' · cited by 1IntegrableOn.mono_measure'TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableContinuousENorm · cited by 290ContinuousENormMeasureTheory.Integrable.aestronglyMeasurable · cited by 84Integrable.aestronglyMeas…MeasureTheory.Integrable.hasFiniteIntegral · cited by 29Integrable.hasFiniteInteg…MeasureTheory.AEStronglyMeasurable.mono_measure · cited by 13AEStronglyMeasurable.mono…MeasureTheory.HasFiniteIntegral.mono_measure · cited by 3HasFiniteIntegral.mono_me…Integrable.mono_measureCITED BYCITES

Cites9

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Cited by26

Results whose statement or proof uses this declaration.