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Theorems · Theorem · real analysis

Filter.Tendsto.log

∀ {α : Type u_1} {f : α → ℝ} {l : Filter α} {x : ℝ},
  Filter.Tendsto f l (nhds x) → x ≠ 0 → Filter.Tendsto (fun x => Real.log (f x)) l (nhds (Real.log x))
Defined in
Mathlib.Analysis.SpecialFunctions.Log.Basic
Cited by
3 results in Mathlib
Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousAt.log · cited by 6ContinuousAt.logContinuousWithinAt.log · cited by 3ContinuousWithinAt.logAsymptotics.IsEquivalent.log · cited by 0IsEquivalent.logReal · cited by 25697RealFilter · cited by 8121Filternhds · cited by 5554nhdsFilter.Tendsto · cited by 3814Filter.TendstoReal.log · cited by 939Real.logFilter.Tendsto.comp · cited by 560Tendsto.compContinuousAt.tendsto · cited by 103ContinuousAt.tendstoReal.continuousAt_log · cited by 7Real.continuousAt_logTendsto.logCITED BYCITES

Cites8

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Cited by3

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