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Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.mono_measure

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f : α → β} {ν : MeasureTheory.Measure α},
  MeasureTheory.AEStronglyMeasurable f μ → ν ≤ μ → MeasureTheory.AEStronglyMeasurable f ν
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
13 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace

Around this declaration

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

MeasureTheory.Integrable.mono_measure · cited by 26Integrable.mono_measureMeasureTheory.AEStronglyMeasurable.restrict · cited by 18AEStronglyMeasurable.rest…aestronglyMeasurable_indicator_iff · cited by 8aestronglyMeasurable_indi…MeasureTheory.AEStronglyMeasurable.mono_set · cited by 6AEStronglyMeasurable.mono…MeasureTheory.setIntegral_map · cited by 3MeasureTheory.setIntegral…MeasureTheory.MemLp.mono_measure · cited by 3MemLp.mono_measureaestronglyMeasurable_sum_measure_iff · cited by 3aestronglyMeasurable_sum_…aestronglyMeasurable_iUnion_iff · cited by 2aestronglyMeasurable_iUni…MeasureTheory.Integrable.summable_integral · cited by 2Integrable.summable_integ…MeasureTheory.AEStronglyMeasurable.iUnion · cited by 2AEStronglyMeasurable.iUni…MeasureTheory.VectorMeasure.tendsto_setIntegral_of_L1 · cited by 1VectorMeasure.tendsto_set…MeasureTheory.AEContinuous.hasBoxIntegral · cited by 1AEContinuous.hasBoxIntegr…BddAbove.convolutionExistsAt · cited by 1BddAbove.convolutionExist…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…Filter.Eventually.filter_mono · cited by 84Eventually.filter_monoMeasureTheory.AEStronglyMeasurable.mk · cited by 82AEStronglyMeasurable.mkMeasureTheory.AEStronglyMeasurable.ae_eq_mk · cited by 77AEStronglyMeasurable.ae_e…MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mk · cited by 71AEStronglyMeasurable.stro…MeasureTheory.ae_mono · cited by 22MeasureTheory.ae_monoAEStronglyMeasurable.mono_mea…CITED BYCITES

Cites9

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Cited by13

Results whose statement or proof uses this declaration.