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Theorems · Definition · real analysis

BoxIntegral.TaggedPrepartition.IsSubordinate

{ι : Type u_1} →
  {I : BoxIntegral.Box ι} → [Fintype ι] → BoxIntegral.TaggedPrepartition I → ((ι → ℝ) → ↑(Set.Ioi 0)) → Prop

A tagged partition π is subordinate to r : (ι → ℝ) → ℝ if each box J ∈ π is included in the closed ball with center π.tag J and radius r (π.tag J).

Defined in
Mathlib.Analysis.BoxIntegral.Partition.Tagged
Cited by
15 results in Mathlib
Foundations
Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Fintype

Around this declaration

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

BoxIntegral.IntegrationParams.MemBaseSet.isSubordinate · cited by 9MemBaseSet.isSubordinateBoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq · cited by 6Prepartition.exists_tagge…BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged · cited by 3TaggedPrepartition.isSubo…BoxIntegral.TaggedPrepartition.IsSubordinate.mono' · cited by 2IsSubordinate.mono'BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eq · cited by 2IntegrationParams.exists_…BoxIntegral.unitPartition.prepartition_isSubordinate · cited by 1unitPartition.prepartitio…tendsto_tsum_div_pow_atTop_integral · cited by 1tendsto_tsum_div_pow_atTo…BoxIntegral.TaggedPrepartition.isSubordinate_single · cited by 1TaggedPrepartition.isSubo…BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition · cited by 1IsSubordinate.biUnionPrep…BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion · cited by 1IsSubordinate.disjUnionBoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition · cited by 1IsSubordinate.infPreparti…BoxIntegral.TaggedPrepartition.IsSubordinate.mono · cited by 1IsSubordinate.monoBoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic · cited by 1Box.exists_taggedPartitio…BoxIntegral.Prepartition.isSubordinate_toSubordinate · cited by 1Prepartition.isSubordinat…BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le · cited by 0IsSubordinate.diam_leDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealFintype · cited by 7736FintypeSet.Elem · cited by 7166Set.ElemSet.Ioi · cited by 1463Set.IoiMetric.closedBall · cited by 704Metric.closedBallBoxIntegral.Box · cited by 464BoxIntegral.BoxBoxIntegral.TaggedPrepartition · cited by 126BoxIntegral.TaggedPrepart…BoxIntegral.Box.Icc · cited by 76Box.IccBoxIntegral.TaggedPrepartition.tag · cited by 34TaggedPrepartition.tagTaggedPrepartition.IsSubordin…CITED BYCITES

Cites10

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

Cited by17

Results whose statement or proof uses this declaration.