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- Cited by
- 11 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ContinuousConstSMulstatement and proof · cited by 832
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.AEStronglyMeasurable.mkproof · cited by 82
- MeasureTheory.AEStronglyMeasurable.ae_eq_mkproof · cited by 77
- MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mkproof · cited by 71
- Filter.EventuallyEq.const_smulproof · cited by 9
- MeasureTheory.StronglyMeasurable.const_smulproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.smulproof · cited by 21
- MeasureTheory.MemLp.const_smulproof · cited by 11
- MeasureTheory.AEStronglyMeasurable.fun_const_smulproof · cited by 4
- MeasureTheory.uniformIntegrable_averageproof · cited by 2
- aestronglyMeasurable_const_smul_iffproof · cited by 1
- MeasureTheory.Integrable.smul_enormproof · cited by 1
- hasFDerivAt_integral_of_dominated_loc_of_lip'proof · cited by 1
- MeasureTheory.lpNorm_const_smulproof · cited by 1
- MeasureTheory.AEEqFun.smul_mkstatement · cited by 0
- ProbabilityTheory.strong_law_Lpproof · cited by 0
- MeasureTheory.MemLp.const_smul'proof · cited by 0