Theorems · Theorem · measure theory

MeasureTheory.Measure.hausdorffMeasure_apply

∀ {X : Type u_2} [inst : EMetricSpace X] [inst_1 : MeasurableSpace X] [inst_2 : BorelSpace X] (d : ℝ) (s : Set X),
  (MeasureTheory.Measure.hausdorffMeasure d) s =
    ⨆ r,
      ⨆ (_ : 0 < r),
        ⨅ t,
          ⨅ (_ : s ⊆ ⋃ n, t n),
            ⨅ (_ : ∀ (n : ℕ), Metric.ediam (t n) ≤ r), ∑' (n : ℕ), ⨆ (_ : (t n).Nonempty), Metric.ediam (t n) ^ d

A formula for μH[d] s.

Defined in

Mathlib.MeasureTheory.Measure.Hausdorff

Cited by

4 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpaceMeasurableSpaceBorelSpace