Theorems · Theorem · measure theory

MeasureTheory.exists_setLAverage_le

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f : α → ENNReal},
  μ s ≠ 0 → MeasureTheory.NullMeasurableSet s μ → ∫⁻ (a : α) in s, f a ∂μ ≠ ⊤ → ∃ x ∈ s, ⨍⁻ (a : α) in s, f a ∂μ ≤ f x

First moment method. The maximum of a measurable function is greater than its mean.

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

0 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound