Theorems · Theorem · measure theory

MeasureTheory.MemLp.of_le_mul

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] {f : α → E} {g : α → F} {c : ℝ},
  MeasureTheory.MemLp g p μ →
    MeasureTheory.AEStronglyMeasurable f μ → (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ c * ‖g x‖) → MeasureTheory.MemLp f p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity

Cited by

7 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup