Theorems · Theorem · sequences and series

tprod_mulIndicator_of_disjoint_on_mulSupport_of_mem

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid 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.mulSupport f) → ∏' (d : γ), (s d).mulIndicator 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

CommMonoidTopologicalSpace