Theorems · Theorem · functional analysis

MeasureTheory.L2.mem_L1_inner

∀ {α : Type u_1} {E : Type u_2} {𝕜 : Type u_4} [inst : RCLike 𝕜] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E] (f g : ↥(MeasureTheory.Lp E 2 μ)),
  MeasureTheory.AEEqFun.mk (fun x => inner 𝕜 (↑↑f x) (↑↑g x)) ⋯ ∈ MeasureTheory.Lp 𝕜 1 μ

Defined in

Mathlib.MeasureTheory.Function.L2Space

Cited by

1 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace