Theorems · Theorem · measure theory

MeasureTheory.setIntegral_condExp_le_of_ae_restrict_nonneg

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
  MeasurableSet s → ∀ {f : α → ℝ}, 0 ≤ᵐ[μ.restrict s] f → ∫ (x : α) in s, μ[f | m] x ∂μ ≤ ∫ (x : α) in s, f x ∂μ

Note that this is not trivial as we don't assume that f is integrable.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Real

Cited by

1 results in Mathlib

Foundations

Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound