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Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.edist_nearestPt_le

∀ {α : Type u_1} [inst : MeasurableSpace α] [inst_1 : PseudoEMetricSpace α] [inst_2 : OpensMeasurableSpace α]
  (e : ℕ → α) (x : α) {k N : ℕ}, k ≤ N → edist ((MeasureTheory.SimpleFunc.nearestPt e N) x) x ≤ edist (e k) x
Defined in
Mathlib.MeasureTheory.Function.SimpleFuncDense
Cited by
2 results in Mathlib
Foundations
Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpacePseudoEMetricSpaceOpensMeasurableSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.SimpleFunc.edist_approxOn_mono · cited by 2SimpleFunc.edist_approxOn…MeasureTheory.SimpleFunc.tendsto_nearestPt · cited by 1SimpleFunc.tendsto_neares…DFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceENNReal · cited by 9879ENNRealLE.le.trans · cited by 3151le.transLT.lt.le · cited by 2189lt.lele_rfl · cited by 1558le_rflPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistOpensMeasurableSpace · cited by 636OpensMeasurableSpaceMeasureTheory.SimpleFunc · cited by 411MeasureTheory.SimpleFuncLE.le.eq_or_lt · cited by 220le.eq_or_ltnonpos_iff_eq_zero · cited by 100nonpos_iff_eq_zeroMeasureTheory.SimpleFunc.nearestPt · cited by 5SimpleFunc.nearestPtMeasureTheory.SimpleFunc.nearestPtInd_succ · cited by 2SimpleFunc.nearestPtInd_s…SimpleFunc.edist_nearestPt_leCITED BYCITES

Cites14

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Cited by2

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