Theorems · Theorem · measure theory
MeasureTheory.memLp_one_iff_integrable
∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
[inst_1 : ContinuousENorm ε] {f : α → ε}, MeasureTheory.MemLp f 1 μ ↔ MeasureTheory.Integrable f μ- Cited by
- 73 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topproof · cited by 9,680
- MeasureTheory.Integrablestatement · cited by 1,367
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.AEStronglyMeasurableproof · cited by 755
- ENorm.enormproof · cited by 715
- MeasureTheory.MemLpstatement and proof · cited by 457
- ContinuousENormstatement and proof · cited by 290
- MeasureTheory.eLpNorm_one_eq_lintegral_enormproof · cited by 16
Cited by73
Results whose statement or proof uses this declaration.
- MeasureTheory.L1.SimpleFunc.integrableproof · cited by 21
- MeasureTheory.MemLp.integrableproof · cited by 14
- MeasureTheory.L1.integrable_coeFnproof · cited by 11
- ProbabilityTheory.IsGaussian.integrable_idproof · cited by 11
- MeasureTheory.SimpleFunc.integrable_iffproof · cited by 8
- MeasureTheory.Integrable.smul_measureproof · cited by 8
- MeasureTheory.integrable_toReal_of_lintegral_ne_topproof · cited by 8
- ProbabilityTheory.HasGaussianLaw.integrableproof · cited by 7
- MeasureTheory.Integrable.smul_of_top_leftproof · cited by 6
- MeasureTheory.MemLp.integrable_mulproof · cited by 6
- ProbabilityTheory.Kernel.integrable_densityproof · cited by 6
- MeasureTheory.Integrable.smul_of_top_rightproof · cited by 5