Theorems · Theorem · measure theory
MeasureTheory.AEStronglyMeasurable.const_mul
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
{f : α → β} [inst_1 : Mul β] [ContinuousMul β],
MeasureTheory.AEStronglyMeasurable f μ → ∀ (c : β), MeasureTheory.AEStronglyMeasurable (fun x => c * f x) μ- Cited by
- 22 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- ContinuousMulstatement and proof · cited by 343
- MeasureTheory.aestronglyMeasurable_constproof · cited by 44
- MeasureTheory.AEStronglyMeasurable.mulproof · cited by 19
Cited by22
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussian.memLp_idproof · cited by 4
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- ProbabilityTheory.complexMGF_id_mapproof · cited by 3
- ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
- ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mulproof · cited by 3
- ProbabilityTheory.integrable_exp_mul_abs_addproof · cited by 2
- integrable_cexp_neg_mul_sqproof · cited by 2
- ProbabilityTheory.integrable_rpow_abs_mul_exp_add_of_integrable_exp_mulproof · cited by 2
- MeasureTheory.Measure.ext_of_complexMGF_eqproof · cited by 1
- GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1
- ProbabilityTheory.HasSubgaussianMGF.id_map_iffproof · cited by 1
- tendsto_integral_comp_smul_smul_of_integrableproof · cited by 1