Theorems · Theorem · sequences and series
summable_finsetProd_of_summable_norm
∀ {ι : Type u_1} {R : Type u_2} [inst : NormedCommRing R] [NormOneClass R] {f : ι → R} [CompleteSpace R],
(Summable fun i => ‖f i‖) → Summable fun s => ∏ i ∈ s, f i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Norm.normstatement and proof · cited by 5,413
- CompleteSpacestatement and proof · cited by 2,532
- Finset.prodstatement · cited by 2,356
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- norm_nonnegproof · cited by 725
- NormedCommRingstatement and proof · cited by 218
- NormOneClassstatement and proof · cited by 136
- Summable.of_norm_boundedproof · cited by 25
- Finset.norm_prod_leproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- tendsto_tprod_one_add_of_dominated_convergenceproof · cited by 1
- summable_finset_prod_of_summable_normproof · cited by 0