Theorems · Theorem · measure theory

MeasureTheory.lintegral_eq_const

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [MeasureTheory.IsProbabilityMeasure μ]
  {f : α → ENNReal} {c : ENNReal}, (∀ᵐ (x : α) ∂μ, f x = c) → ∫⁻ (x : α), f x ∂μ = c

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Countable

Cited by

3 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasureTheory.IsProbabilityMeasure