Theorems · Theorem · sequences and series
hasSum_fintype
∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] [inst_2 : Fintype β] (f : β → α)
(L : optParam (SummationFilter β) (SummationFilter.unconditional β)) [L.LeAtTop], HasSum f (∑ b, f b) L- Cited by
- 15 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement · cited by 2,068
- SummationFilterstatement and proof · cited by 607
- HasSumstatement and proof · cited by 518
- SummationFilter.LeAtTopstatement and proof · cited by 80
- Set.toFinset_congrproof · cited by 33
- SummationFilter.support_eq_univproof · cited by 10
Cited by15
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_one_div_norm_rpowproof · cited by 4
- Complex.hasSum_cos'proof · cited by 3
- Complex.hasSum_sin'proof · cited by 3
- summable_sum_mul_antidiagonal_of_summable_mulproof · cited by 3
- FormalMultilinearSeries.changeOriginSeries_summable_aux₁proof · cited by 3
- Summable.tsum_mul_tsum_eq_tsum_sum_antidiagonalproof · cited by 3
- Memℓp.allproof · cited by 2
- HasFPowerSeriesWithinAt.compproof · cited by 2
- FormalMultilinearSeries.comp_summable_nnrealproof · cited by 2
- Complex.hasSum_arctanproof · cited by 1
- MeasureTheory.VectorMeasure.hasSum_setIntegral_iUnionproof · cited by 1
- FormalMultilinearSeries.changeOrigin_evalproof · cited by 1