Theorems · Theorem · measure theory

MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto

∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [inst_2 : OpensMeasurableSpace Ω]
  {γ : Type u_3} {F : Filter γ} {μs : γ → MeasureTheory.FiniteMeasure Ω} {μ : MeasureTheory.FiniteMeasure Ω},
  Filter.Tendsto μs F (nhds μ) ↔
    ∀ (f : BoundedContinuousFunction Ω NNReal),
      Filter.Tendsto (fun i => (μs i).toWeakDualBCNN f) F (nhds (μ.toWeakDualBCNN f))

Defined in

Mathlib.MeasureTheory.Measure.FiniteMeasure

Cited by

2 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpace