Theorems · Theorem · measure theory

MeasureTheory.ae_eq_of_ae_le_of_lintegral_le

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
  f ≤ᵐ[μ] g → ∫⁻ (x : α), f x ∂μ ≠ ⊤ → AEMeasurable g μ → ∫⁻ (x : α), g x ∂μ ≤ ∫⁻ (x : α), f x ∂μ → f =ᵐ[μ] g

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Markov

Cited by

3 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound