Theorems · Theorem · measure theory

MeasureTheory.lintegral_add_mul_meas_add_le_le_lintegral

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
  f ≤ᵐ[μ] g → AEMeasurable g μ → ∀ (ε : ENNReal), ∫⁻ (a : α), f a ∂μ + ε * μ {x | f x + ε ≤ g x} ≤ ∫⁻ (a : α), g a ∂μ

A version of Markov's inequality for two functions. It doesn't follow from the standard Markov's inequality because we only assume measurability of g, not f.

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Markov

Cited by

2 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound