Theorems · Theorem · complex analysis
Function.locallyFinsuppWithin.logCounting_single_isBigO_log
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : DecidableEq E] [inst_2 : ProperSpace E] {e : E} {n : ℤ},
Function.locallyFinsuppWithin.logCounting (Function.locallyFinsuppWithin.single e n) =O[Filter.atTop] Real.logThe logarithmic counting function of a singleton is big-O of log. This is the qualitative
consequence of logCounting_single_eq_log_sub_const.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- Set.univstatement · cited by 3,945
- AddMonoidHomstatement · cited by 3,230
- Filter.atTopstatement and proof · cited by 2,405
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Real.logstatement and proof · cited by 939
- Asymptotics.IsBigOstatement and proof · cited by 506
Cited by1
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.logCounting_isBigO_log_of_finite_supportproof · cited by 1