Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.tendsto_iff_weakDual_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) ↔ Filter.Tendsto (fun i => (μs i).toWeakDualBCNN) F (nhds μ.toWeakDualBCNN)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- NNRealstatement · cited by 4,310
- Filter.Tendstostatement · cited by 3,814
- OpensMeasurableSpacestatement and proof · cited by 636
- BoundedContinuousFunctionstatement · cited by 511
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- WeakDualstatement · cited by 103
- Topology.IsInducing.tendsto_nhds_iffproof · cited by 15
- MeasureTheory.FiniteMeasure.toWeakDualBCNNstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendstoproof · cited by 2