Theorems · Theorem · measure theory
MeasureTheory.Integrable.const_mul
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {𝕜 : Type u_8} [inst : NormedRing 𝕜] {f : α → 𝕜},
MeasureTheory.Integrable f μ → ∀ (c : 𝕜), MeasureTheory.Integrable (fun x => c * f x) μ- Cited by
- 58 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- NormedRingstatement and proof · cited by 924
- MeasureTheory.Integrable.smulproof · cited by 21
Cited by58
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.integrable_compproof · cited by 25
- Asymptotics.IsBigO.integrableAtFilterproof · cited by 7
- MeasureTheory.Integrable.convolution_integrandproof · cited by 6
- CircleIntegrable.outproof · cited by 5
- VectorFourier.hasFDerivAt_fourierIntegralproof · cited by 5
- ProbabilityTheory.integrable_gaussianPDFRealproof · cited by 4
- ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExpproof · cited by 3
- MeasureTheory.condExp_stronglyMeasurable_bilin_of_boundproof · cited by 3
- VectorFourier.integrable_fourierPowSMulRightproof · cited by 3
- MeasureTheory.ext_of_integral_char_eqproof · cited by 3
- integrable_rpow_neg_one_add_norm_sqproof · cited by 2
- BddAbove.continuous_convolution_right_of_integrableproof · cited by 2