Theorems · Theorem · complex analysis
Complex.IsExpCmpFilter.isLittleO_log_norm_re
∀ {l : Filter ℂ}, Complex.IsExpCmpFilter l → (fun z => Real.log ‖z‖) =o[l] Complex.reIf l : Filter ℂ is an "exponential comparison filter", then $\log |z| =o(ℜ z)$ along l.
This is the main lemma in the proof of Complex.IsExpCmpFilter.isLittleO_cpow_exp below.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites52
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
- Filterstatement and proof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- absproof · cited by 1,814
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- LT.lt.ne'proof · cited by 1,417
- le_transproof · cited by 985
- Real.logstatement and proof · cited by 939
Cited by1
Results whose statement or proof uses this declaration.
- Complex.IsExpCmpFilter.isLittleO_cpow_expproof · cited by 1