Mathlib Map

Theorems · Theorem · measure theory

Measurable.mul

∀ {M : Type u_2} {α : Type u_3} [inst : MeasurableSpace M] [inst_1 : Mul M] {m : MeasurableSpace α} {f g : α → M}
  [MeasurableMul₂ M], Measurable f → Measurable g → Measurable (f * g)
Defined in
Mathlib.MeasureTheory.Group.Arithmetic
Cited by
29 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMulMeasurableMul₂

Around this declaration

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

Measurable.fun_mul · cited by 30Measurable.fun_mulFinset.measurable_prod · cited by 11Finset.measurable_prodMeasureTheory.quasiMeasurePreserving_inv · cited by 7MeasureTheory.quasiMeasur…ProbabilityTheory.Kernel.iIndepFun.indepFun_mul_left · cited by 3iIndepFun.indepFun_mul_le…Finset.measurable_fun_prod · cited by 3Finset.measurable_fun_prodProbabilityTheory.avgRisk_countable' · cited by 3ProbabilityTheory.avgRisk…MeasureTheory.measure_add_lintegral_eq · cited by 3MeasureTheory.measure_add…ProbabilityTheory.measurable_gammaPDFReal · cited by 3ProbabilityTheory.measura…MeasureTheory.measure_mul_lintegral_eq · cited by 3MeasureTheory.measure_mul…integrable_rpow_mul_exp_neg_mul_sq · cited by 2integrable_rpow_mul_exp_n…ProbabilityTheory.Kernel.iIndepFun.indepFun_mul_left₀ · cited by 2iIndepFun.indepFun_mul_le…MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable · cited by 2MeasureTheory.lintegral_w…List.measurable_prod · cited by 2List.measurable_prodMeasureTheory.measurePreserving_prod_mul_right · cited by 2MeasureTheory.measurePres…NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral · cited by 1mixedEmbedding.volume_eq_…MeasurableSpace · cited by 13106MeasurableSpaceMeasurable · cited by 1499MeasurableMeasurable.comp · cited by 234Measurable.compMeasurableMul₂ · cited by 139MeasurableMul₂Measurable.prodMk · cited by 115Measurable.prodMkMeasurableMul₂.measurable_mul · cited by 8MeasurableMul₂.measurable…Measurable.mulCITED BYCITES

Cites6

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

Cited by29

Results whose statement or proof uses this declaration.