Mathlib Map

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
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
22 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceMulContinuousMul

Around this declaration

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

ProbabilityTheory.IsGaussian.memLp_id · cited by 4IsGaussian.memLp_idindicator_indepFun_pi_of_prod_bcf · cited by 4indicator_indepFun_pi_of_…ProbabilityTheory.complexMGF_id_map · cited by 3ProbabilityTheory.complex…ProbabilityTheory.hasDerivAt_integral_pow_mul_exp · cited by 3ProbabilityTheory.hasDeri…ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mul · cited by 3ProbabilityTheory.integra…ProbabilityTheory.integrable_exp_mul_abs_add · cited by 2ProbabilityTheory.integra…integrable_cexp_neg_mul_sq · cited by 2integrable_cexp_neg_mul_sqProbabilityTheory.integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul · cited by 2ProbabilityTheory.integra…MeasureTheory.Measure.ext_of_complexMGF_eq · cited by 1Measure.ext_of_complexMGF…GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I · cited by 1GaussianFourier.integrabl…ProbabilityTheory.HasSubgaussianMGF.id_map_iff · cited by 1HasSubgaussianMGF.id_map_…tendsto_integral_comp_smul_smul_of_integrable · cited by 1tendsto_integral_comp_smu…ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet · cited by 1ProbabilityTheory.integra…MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun · cited by 1MeasureTheory.measureReal…continuousAt_gaussian_integral · cited by 1continuousAt_gaussian_int…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…ContinuousMul · cited by 343ContinuousMulMeasureTheory.aestronglyMeasurable_const · cited by 44MeasureTheory.aestronglyM…MeasureTheory.AEStronglyMeasurable.mul · cited by 19AEStronglyMeasurable.mulAEStronglyMeasurable.const_mulCITED BYCITES

Cites7

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

Cited by22

Results whose statement or proof uses this declaration.