Theorems · Theorem · measure theory

MeasureTheory.Integrable.integral_eq_integral_meas_le

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {f : α → ℝ},
  MeasureTheory.Integrable f μ → 0 ≤ᵐ[μ] f → ∫ (ω : α), f ω ∂μ = ∫ (t : ℝ) in Set.Ioi 0, μ.real {a | t ≤ f a}

Defined in

Mathlib.MeasureTheory.Integral.Layercake

Cited by

1 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace