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7 changes: 7 additions & 0 deletions FormalizingGMT/Project Versions/Definitions.lean
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Expand Up @@ -72,6 +72,13 @@ noncomputable def density_ratio
(E ∩ EMetric.closedBall x (ENNReal.ofReal r)) /
(ENNReal.ofReal (2 * r)) ^ s

noncomputable def density_ratio_radon
{X : Type*} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X]
(μ : MeasureTheory.Measure X)
(E : Set X) (x : X) (r : ℝ) : ENNReal :=
μ (E ∩ EMetric.closedBall x (ENNReal.ofReal r)) /
μ (EMetric.closedBall x (ENNReal.ofReal r))

noncomputable def upper_density
{X : Type*} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X]
(E : Set X) (s : ℝ) (x : X) : ENNReal :=
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