Theorems · Theorem · measure theory

HasOuterApproxClosed.measure_le_lintegral

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : HasOuterApproxClosed X] {F : Set X} (hF : IsClosed F)
  [inst_2 : MeasurableSpace X] [OpensMeasurableSpace X] (μ : MeasureTheory.Measure X) (n : ℕ),
  μ F ≤ ∫⁻ (x : X), ↑((hF.apprSeq n) x) ∂μ

The measure of a closed set is at most the integral of any function in a decreasing approximating sequence to the indicator of the set.

Defined in

Mathlib.MeasureTheory.Measure.HasOuterApproxClosed

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceHasOuterApproxClosedMeasurableSpaceOpensMeasurableSpace