Theorems · Theorem · sequences and series
summable_one_div_pow_of_le
∀ {m : ℝ} {f : ℕ → ℕ}, 1 < m → (∀ (i : ℕ), i ≤ f i) → Summable fun i => 1 / m ^ f iA series whose terms are bounded by the terms of a converging geometric series converges.
- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalstatement · cited by 2,068
- le_of_ltproof · cited by 1,175
- LE.le.trans_ltproof · cited by 795
- Summablestatement · cited by 778
- Eq.leproof · cited by 605
- zero_lt_oneproof · cited by 598
- one_powproof · cited by 521
- LT.lt.transproof · cited by 370
Cited by2
Results whose statement or proof uses this declaration.
- LiouvilleNumber.summableproof · cited by 2
- LiouvilleNumber.remainder_lt'proof · cited by 1