Theorems · Theorem · functional analysis
MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top
∀ {α : Type u_1} {F : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup F]
(f : ↥(MeasureTheory.Lp F 2 μ)), MeasureTheory.eLpNorm (fun x => ‖↑↑f x‖ ^ 2) 1 μ < ⊤- Defined in
- Mathlib.MeasureTheory.Function.L2Space
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 223 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.
Cites20
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
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- one_mulproof · cited by 2,841
- ENNReal.ofRealproof · cited by 863
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.L2.eLpNorm_inner_lt_topproof · cited by 1