Theorems · Theorem · sequences and series
summable_finsetProd_of_summable_nonneg
∀ {ι : Type u_1} {f : ι → ℝ}, (∀ (i : ι), 0 ≤ f i) → Summable f → Summable fun s => ∏ i ∈ s, f i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- Finset.biUnionproof · cited by 217
- Finset.powersetproof · cited by 93
- Finset.prod_nonnegproof · cited by 39
- Finset.sum_le_sum_of_subset_of_nonnegproof · cited by 31
- Finset.mem_powersetproof · cited by 26
- Real.exp_le_expproof · cited by 16
- Summable.sum_le_tsumproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- summable_finsetProd_of_summable_normproof · cited by 2
- tendsto_tprod_one_add_of_dominated_convergenceproof · cited by 1
- summable_finset_prod_of_summable_nonnegproof · cited by 0