Theorems · Theorem · functional analysis

MeasureTheory.Lp.pow_mul_meas_ge_le_enorm

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] (f : ↥(MeasureTheory.Lp E p μ)),
  p ≠ 0 → p ≠ ⊤ → ∀ (ε : ENNReal), (ε * μ {x | ε ≤ ‖↑↑f x‖ₑ ^ p.toReal}) ^ (1 / p.toReal) ≤ ENNReal.ofReal ‖f‖

A version of Markov's inequality with elements of Lp.

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroup