Theorems · Theorem · sequences and series
tsum_univ
∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] (f : β → α),
∑' (x : ↑Set.univ), f ↑x = ∑' (x : β), f x- Cited by
- 6 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemstatement · cited by 7,166
- Set.univstatement · cited by 3,945
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- Function.supportproof · cited by 610
- Set.subset_univproof · cited by 228
- tsum_subtype_eq_of_support_subsetproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- ENNReal.tsum_constproof · cited by 2
- MeasureTheory.Measure.inf_applyproof · cited by 2
- NumberField.Set.HasDirichletDensity.le_oneproof · cited by 1
- ENNReal.tsum_oneproof · cited by 1
- tsum_rangeproof · cited by 0
- ENNReal.tsum_biUnionproof · cited by 0