Theorems · Theorem · measure theory

MeasureTheory.integral_eq_iff_of_ae_le

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ℝ},
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g μ → f ≤ᵐ[μ] g → (∫ (a : α), f a ∂μ = ∫ (a : α), g a ∂μ ↔ f =ᵐ[μ] g)

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

0 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound