Theorems · Theorem · functional analysis

MeasureTheory.Lp.norm_le_mul_norm_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 : ℝ} {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 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup