Theorems · Theorem · functional analysis
MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top
∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] {f : α →ₘ[μ] E}, f ∈ MeasureTheory.Lp E p μ ↔ MeasureTheory.eLpNorm (↑f) p μ < ⊤- Cited by
- 2 results in Mathlib
- Foundations
- Depth 221 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.eLpNormstatement · cited by 329
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.AEEqFun.compMeasurePreserving_mem_Lpproof · cited by 0
- MeasureTheory.Lp.const_smul_mem_Lpproof · cited by 0