Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.tendsto_nearestPt

∀ {α : Type u_1} [inst : MeasurableSpace α] [inst_1 : PseudoEMetricSpace α] [inst_2 : OpensMeasurableSpace α]
  {e : ℕ → α} {x : α},
  x ∈ closure (Set.range e) → Filter.Tendsto (fun N => (MeasureTheory.SimpleFunc.nearestPt e N) x) Filter.atTop (nhds x)

Defined in: Mathlib.MeasureTheory.Function.SimpleFuncDense
Cited by: 1 results in Mathlib
Foundations: Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace PseudoEMetricSpace OpensMeasurableSpace

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Cites22

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
ENNRealproof · cited by 9,879
nhdsstatement · cited by 5,554
Set.rangestatement and proof · cited by 4,705
Filter.Tendstostatement · cited by 3,814
Filter.atTopstatement · cited by 2,405
PseudoEMetricSpacestatement and proof · cited by 1,536
closurestatement and proof · cited by 1,254
Set.Iciproof · cited by 1,070
LE.le.trans_ltproof · cited by 795

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.SimpleFunc.tendsto_approxOnproof · cited by 6