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Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.add

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f g : α → β} [inst_1 : Add β] [ContinuousAdd β],
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable g μ → MeasureTheory.AEStronglyMeasurable (f + g) μ
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
12 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddContinuousAdd

Around this declaration

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

MeasureTheory.Integrable.add · cited by 42Integrable.addMeasureTheory.MemLp.add · cited by 24MemLp.addMeasureTheory.AEStronglyMeasurable.fun_add · cited by 2AEStronglyMeasurable.fun_…MeasureTheory.eLpNorm_sum_le · cited by 2MeasureTheory.eLpNorm_sum…MeasureTheory.AEStronglyMeasurable.add_const · cited by 2AEStronglyMeasurable.add_…MeasureTheory.AEStronglyMeasurable.add_iff_right · cited by 2AEStronglyMeasurable.add_…List.aestronglyMeasurable_sum · cited by 2List.aestronglyMeasurable…MeasureTheory.AEEqFun.Integrable.add · cited by 1Integrable.addMeasureTheory.aestronglyMeasurable_condExpL1CLM · cited by 1MeasureTheory.aestronglyM…MeasureTheory.AEStronglyMeasurable.const_add · cited by 1AEStronglyMeasurable.cons…MeasureTheory.AEEqFun.mk_add_mk · cited by 0AEEqFun.mk_add_mkMeasureTheory.eLpNorm'_sum_le · cited by 0MeasureTheory.eLpNorm'_su…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureContinuousAdd · cited by 777ContinuousAddMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…MeasureTheory.AEStronglyMeasurable.mk · cited by 82AEStronglyMeasurable.mkMeasureTheory.AEStronglyMeasurable.ae_eq_mk · cited by 77AEStronglyMeasurable.ae_e…MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mk · cited by 71AEStronglyMeasurable.stro…Filter.EventuallyEq.add · cited by 23EventuallyEq.addMeasureTheory.StronglyMeasurable.add · cited by 10StronglyMeasurable.addAEStronglyMeasurable.addCITED BYCITES

Cites10

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Cited by12

Results whose statement or proof uses this declaration.