Theorems · Theorem · sequences and series
ENNReal.exists_pos_sum_of_countable
∀ {ε : ENNReal}, ε ≠ 0 → ∀ (ι : Type u_4) [Countable ι], ∃ ε', (∀ (i : ι), 0 < ε' i) ∧ ∑' (i : ι), ↑(ε' i) < ε- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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.
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- LT.lt.ne'proof · cited by 1,417
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- tsumstatement · cited by 1,148
- Countablestatement and proof · cited by 633
- HasSumproof · cited by 518
- pos_iff_ne_zeroproof · cited by 180
- lt_transproof · cited by 165
- exists_betweenproof · cited by 102
- ENNReal.coe_lt_coeproof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.exists_pos_sum_of_countable'proof · cited by 5
- ENNReal.exists_pos_tsum_mul_lt_of_countableproof · cited by 2
- StieltjesFunction.outer_Iocproof · cited by 2
- StieltjesFunction.outer_trimproof · cited by 0