Theorems · Theorem · sequences and series

tsum_indicator_of_disjoint_on_support_of_mem

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] (s : γ → Set β)
  (f : β → α),
  ∀ i ∈ ⋃ d, s d,
    Pairwise (Function.onFun Disjoint fun j => s j ∩ Function.support f) → ∑' (d : γ), (s d).indicator f i = f i

Defined in: Mathlib.Topology.Algebra.InfiniteSum.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid TopologicalSpace

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Cites20

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

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
AddCommMonoidstatement and proof · cited by 12,281
Set.Elemproof · cited by 7,166
Set.iUnionstatement and proof · cited by 2,483
Finset.sum_congrproof · cited by 2,323
Disjointstatement and proof · cited by 2,201
SummationFilter.unconditionalstatement · cited by 2,068
tsumstatement · cited by 1,148
Set.indicatorstatement and proof · cited by 723
Function.supportstatement and proof · cited by 610
Function.onFunstatement and proof · cited by 570

Cited by2

Results whose statement or proof uses this declaration.

indicator_iUnion_of_pairwise_disjoint_on_supportproof · cited by 1
tsum_indicator_of_mem_union_disjointproof · cited by 0