Theorems · Theorem · real analysis
tendsto_log_mul_rpow_nhdsGT_zero
∀ {r : ℝ}, 0 < r → Filter.Tendsto (fun x => Real.log x * x ^ r) (nhdsWithin 0 (Set.Ioi 0)) (nhds 0)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- LT.lt.leproof · cited by 2,189
- nhdsWithinstatement · cited by 1,912
- Set.Ioistatement and proof · cited by 1,463
- Real.logstatement and proof · cited by 939
- Filter.Eventually.monoproof · cited by 646
- Filter.Tendsto.congr'proof · cited by 154
- div_inv_eq_mulproof · cited by 53
- Membership.mem.outproof · cited by 38
- Real.rpow_negproof · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- Real.continuous_mul_logproof · cited by 9
- tendsto_log_mul_self_nhdsLT_zeroproof · cited by 2
- integral_log_from_zero_of_posproof · cited by 1