Theorems · Theorem · measure theory

MeasureTheory.Integrable.measure_norm_ge_lt_top

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {f : α → β}, MeasureTheory.Integrable f μ → ∀ {ε : ℝ}, 0 < ε → μ {x | ε ≤ ‖f x‖} < ⊤

A non-quantitative version of Markov inequality for integrable functions: the measure of points where ‖f x‖ ≥ ε is finite for all positive ε.

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

3 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup