Theorems · Theorem · measure theory
MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [inst_2 : OpensMeasurableSpace Ω]
{δ : Type u_2} (F : Filter δ) {μs : δ → MeasureTheory.ProbabilityMeasure Ω} {μ₀ : MeasureTheory.ProbabilityMeasure Ω},
Filter.Tendsto μs F (nhds μ₀) ↔
Filter.Tendsto (MeasureTheory.ProbabilityMeasure.toFiniteMeasure ∘ μs) F (nhds μ₀.toFiniteMeasure)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- OpensMeasurableSpacestatement and proof · cited by 636
- MeasureTheory.FiniteMeasurestatement · cited by 150
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- MeasureTheory.ProbabilityMeasure.toFiniteMeasurestatement · cited by 26
- Topology.IsEmbedding.tendsto_nhds_iffproof · cited by 13
- MeasureTheory.ProbabilityMeasure.toFiniteMeasure_isEmbeddingproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendstoproof · cited by 3
- MeasureTheory.ProbabilityMeasure.limsup_measure_closed_le_of_tendstoproof · cited by 1
- MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendstoproof · cited by 1