Theorems · Theorem · measure theory
MeasureTheory.AEStronglyMeasurable.norm
∀ {α : Type u_1} {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_5} [inst : SeminormedAddCommGroup β]
{f : α → β}, MeasureTheory.AEStronglyMeasurable f μ → MeasureTheory.AEStronglyMeasurable (fun x => ‖f x‖) μ- Cited by
- 30 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- Continuous.comp_aestronglyMeasurableproof · cited by 77
- continuous_normproof · cited by 36
Cited by30
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.normproof · cited by 63
- MeasureTheory.norm_integral_le_integral_normproof · cited by 25
- MeasureTheory.integrable_norm_iffproof · cited by 19
- ProbabilityTheory.integrable_comp_iffproof · cited by 6
- MeasureTheory.Integrable.convolution_integrandproof · cited by 6
- MeasureTheory.AECover.integrable_of_integral_norm_boundedproof · cited by 6
- MeasureTheory.integrable_prod_iffproof · cited by 5
- MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_normproof · cited by 4
- ProbabilityTheory.IsGaussian.memLp_idproof · cited by 4
- MeasureTheory.MemLp.normproof · cited by 3
- ProbabilityTheory.integrable_compProd_iffproof · cited by 3
- MeasureTheory.integral_norm_eq_lintegral_enormproof · cited by 3