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Linglib.Core.MeasureTheory.Measure.AbsolutelyContinuous

Absolute continuity on a countable type #

On a countable type with measurable singletons, absolute continuity is checked on atoms. [UPSTREAM] candidate for Mathlib/MeasureTheory/Measure/AbsolutelyContinuous.lean.

theorem MeasureTheory.Measure.absolutelyContinuous_of_forall_singleton {α : Type u_1} [MeasurableSpace α] [Countable α] {μ ν : Measure α} (h : ∀ (a : α), ν {a} = 0μ {a} = 0) :
μ.AbsolutelyContinuous ν
theorem MeasureTheory.Measure.absolutelyContinuous_iff_forall_singleton {α : Type u_1} [MeasurableSpace α] [Countable α] {μ ν : Measure α} :
μ.AbsolutelyContinuous ν ∀ (a : α), ν {a} = 0μ {a} = 0