Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.tendsto_iff_forall_testAgainstNN_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).testAgainstNN f) F (nhds (μ.testAgainstNN f))- Cited by
- 5 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 and proof · cited by 5,554
- NNRealstatement and proof · cited by 4,310
- Filter.Tendstostatement and proof · cited by 3,814
- OpensMeasurableSpacestatement and proof · cited by 636
- BoundedContinuousFunctionstatement and proof · cited by 511
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.testAgainstNNstatement and proof · cited by 27
- MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendstoproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendstoproof · cited by 1
- MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendstoproof · cited by 1
- MeasureTheory.FiniteMeasure.tendsto_zero_of_tendsto_zero_massproof · cited by 0