Mathlib Map

Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.const_smul

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f : α → β} {𝕜 : Type u_5} [inst_1 : SMul 𝕜 β] [ContinuousConstSMul 𝕜 β],
  MeasureTheory.AEStronglyMeasurable f μ → ∀ (c : 𝕜), MeasureTheory.AEStronglyMeasurable (c • f) μ
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
11 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceSMulContinuousConstSMul

Around this declaration

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

MeasureTheory.Integrable.smul · cited by 21Integrable.smulMeasureTheory.MemLp.const_smul · cited by 11MemLp.const_smulMeasureTheory.AEStronglyMeasurable.fun_const_smul · cited by 4AEStronglyMeasurable.fun_…MeasureTheory.uniformIntegrable_average · cited by 2MeasureTheory.uniformInte…aestronglyMeasurable_const_smul_iff · cited by 1aestronglyMeasurable_cons…MeasureTheory.Integrable.smul_enorm · cited by 1Integrable.smul_enormhasFDerivAt_integral_of_dominated_loc_of_lip' · cited by 1hasFDerivAt_integral_of_d…MeasureTheory.lpNorm_const_smul · cited by 1MeasureTheory.lpNorm_cons…MeasureTheory.AEEqFun.smul_mk · cited by 0AEEqFun.smul_mkProbabilityTheory.strong_law_Lp · cited by 0ProbabilityTheory.strong_…MeasureTheory.MemLp.const_smul' · cited by 0MemLp.const_smul'TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureContinuousConstSMul · cited by 832ContinuousConstSMulMeasureTheory.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.const_smul · cited by 9EventuallyEq.const_smulMeasureTheory.StronglyMeasurable.const_smul · cited by 5StronglyMeasurable.const_…AEStronglyMeasurable.const_sm…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.