Theorems · Theorem · complex analysis
Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_const
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : DecidableEq E] [inst_2 : ProperSpace E] {e : E} {r : ℝ}
{n : ℤ},
‖e‖ ≤ r →
Function.locallyFinsuppWithin.logCounting (Function.locallyFinsuppWithin.single e n) r =
↑n * (Real.log r - Real.log ‖e‖)The logarithmic counting function of a singleton indicator is asymptotically equal to
log · - log ‖e‖.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
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
- SetLike.coeproof · cited by 8,199
- Norm.normstatement and proof · cited by 5,413
- Set.univstatement · cited by 3,945
- AddMonoidHomstatement · cited by 3,230
- LE.le.transproof · cited by 3,151
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
Cited by4
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.one_isLittleO_logCounting_singleproof · cited by 1
- Function.locallyFinsuppWithin.finite_support_of_logCounting_isBigO_logproof · cited by 1
- Function.locallyFinsuppWithin.logCounting_single_isBigO_logproof · cited by 1
- Function.locallyFinsuppWithin.logCounting_strictMonoproof · cited by 1