Theorems · Theorem · measure theory
MeasureTheory.Integrable.norm
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
{f : α → β}, MeasureTheory.Integrable f μ → MeasureTheory.Integrable (fun a => ‖f a‖) μ- Cited by
- 63 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement · cited by 5,413
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.Integrable.aestronglyMeasurableproof · cited by 84
- MeasureTheory.AEStronglyMeasurable.normproof · cited by 30
- MeasureTheory.Integrable.hasFiniteIntegralproof · cited by 29
- MeasureTheory.HasFiniteIntegral.normproof · cited by 1
Cited by63
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.integrable_compproof · cited by 25
- VectorFourier.fourierIntegral_convergent_iffproof · cited by 9
- MeasureTheory.AECover.integral_tendsto_of_countably_generatedproof · cited by 7
- Asymptotics.IsBigO.integrableAtFilterproof · cited by 7
- MeasureTheory.integrable_of_le_of_leproof · cited by 6
- MeasureTheory.Integrable.convolution_integrandproof · cited by 6
- MeasureTheory.Integrable.prodMkproof · cited by 5
- IntervalIntegrable.normproof · cited by 5
- CircleIntegrable.outproof · cited by 5
- hasFDerivAt_integral_of_dominated_loc_of_lipproof · cited by 4
- MeasureTheory.condExp_stronglyMeasurable_bilin_of_boundproof · cited by 3
- Integrable.norm_condExp_rpow_leproof · cited by 3