Mathlib Map

Theorems · Definition · real analysis

BoxIntegral.Prepartition.iUnion

{ι : Type u_1} → {I : BoxIntegral.Box ι} → BoxIntegral.Prepartition I → Set (ι → ℝ)

Given a prepartition π : BoxIntegral.Prepartition I, π.iUnion is the part of I covered by the boxes of π.

Defined in
Mathlib.Analysis.BoxIntegral.Partition.Basic
Cited by
71 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

BoxIntegral.TaggedPrepartition.iUnion · cited by 51TaggedPrepartition.iUnionBoxIntegral.Prepartition.IsPartition.iUnion_eq · cited by 9IsPartition.iUnion_eqBoxIntegral.Prepartition.disjUnion · cited by 7Prepartition.disjUnionBoxIntegral.TaggedPrepartition.unionComplToSubordinate · cited by 7TaggedPrepartition.unionC…BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq · cited by 6Prepartition.exists_tagge…BoxIntegral.Prepartition.isPartition_iff_iUnion_eq · cited by 6Prepartition.isPartition_…BoxIntegral.Prepartition.iUnion_compl · cited by 5Prepartition.iUnion_complBoxIntegral.Prepartition.iUnion_biUnion · cited by 4Prepartition.iUnion_biUni…BoxIntegral.Prepartition.iUnion_subset · cited by 4Prepartition.iUnion_subsetBoxIntegral.Prepartition.iUnion_top · cited by 4Prepartition.iUnion_topBoxIntegral.IntegrationParams.toFilterDistortioniUnion · cited by 4IntegrationParams.toFilte…BoxIntegral.IntegrationParams.MemBaseSet.exists_compl · cited by 3MemBaseSet.exists_complBoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter · cited by 3Prepartition.eventually_s…BoxIntegral.Prepartition.exists_iUnion_eq_sdiff · cited by 3Prepartition.exists_iUnio…BoxIntegral.Prepartition.iUnion_biUnion_partition · cited by 3Prepartition.iUnion_biUni…Set · cited by 53352SetReal · cited by 25697RealSet.iUnion · cited by 2483Set.iUnionBoxIntegral.Box · cited by 464BoxIntegral.BoxBoxIntegral.Prepartition · cited by 199BoxIntegral.PrepartitionBoxIntegral.Box.toSet · cited by 121Box.toSetPrepartition.iUnionCITED BYCITES

Cites6

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

Cited by77

Results whose statement or proof uses this declaration.