Theorems · Theorem · functional analysis

MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul

∀ {α : Type u_1} {E : Type u_4} {F : Type u_5} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] {c : NNReal} {f : ↥(MeasureTheory.Lp E p μ)}
  {g : ↥(MeasureTheory.Lp F p μ)}, (∀ᵐ (x : α) ∂μ, ‖↑↑f x‖₊ ≤ c * ‖↑↑g x‖₊) → ‖f‖₊ ≤ c * ‖g‖₊

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup