Theorems · Theorem · sequences and series
tprod_eq_one_of_not_multipliable
∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {L : SummationFilter β} {f : β → α},
¬Multipliable f L → ∏'[L] (b : β), f b = 1- Cited by
- 14 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CommMonoidstatement and proof · cited by 2,264
- SummationFilterstatement and proof · cited by 607
- tprodstatement · cited by 230
- Multipliablestatement and proof · cited by 213
- tprod_defproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- cauchySeq_finset_iff_tprod_vanishingproof · cited by 3
- IsUltrametricDist.norm_tprod_leproof · cited by 2
- Topology.IsClosedEmbedding.map_tprodproof · cited by 2
- MeasureTheory.StronglyMeasurable.tprodproof · cited by 1
- Measurable.tprodproof · cited by 1
- tendsto_prod_nat_addproof · cited by 0
- one_le_tprodproof · cited by 0
- ArithmeticFunction.isMultiplicative_eulerProductproof · cited by 0
- tprod_le_of_prod_le'proof · cited by 0
- tprod_constproof · cited by 0
- tprod_le_oneproof · cited by 0
- tprod_memproof · cited by 0