Theorems · Theorem · functional analysis

MeasureTheory.MemLp.norm_rpow

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f : α → E},
  MeasureTheory.MemLp f p μ → p ≠ 0 → p ≠ ⊤ → MeasureTheory.MemLp (fun x => ‖f x‖ ^ p.toReal) 1 μ

Defined in: Mathlib.MeasureTheory.Function.LpSpace.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
TopologicalSpaceproof · cited by 24,529
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 and proof · cited by 5,413
ENNReal.toRealstatement and proof · cited by 859
div_eq_mul_invproof · cited by 715
MeasureTheory.MemLpstatement and proof · cited by 457
ENormproof · cited by 155

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.MemLp.integrable_sqproof · cited by 5
MeasureTheory.MemLp.integrable_norm_rpowproof · cited by 3
MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_leproof · cited by 1