Theorems · Theorem · sequences and series
NNReal.exists_pos_sum_of_countable
∀ {ε : NNReal}, ε ≠ 0 → ∀ (ι : Type u_4) [Countable ι], ∃ ε', (∀ (i : ι), 0 < ε' i) ∧ ∃ c, HasSum ε' c ∧ c < ε- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 156 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Countablestatement and proof · cited by 633
- HasSumstatement and proof · cited by 518
- pos_iff_ne_zeroproof · cited by 180
- Encodableproof · cited by 140
- exists_betweenproof · cited by 102
- NNReal.coe_le_coeproof · cited by 73
- LT.lt.trans_le'proof · cited by 52
- NNReal.coe_lt_coeproof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.exists_pos_sum_of_countableproof · cited by 4
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- IsOpen.exists_contDiff_support_eqproof · cited by 2
- BoxIntegral.HasIntegral.of_aeEq_zeroproof · cited by 1