An Analogue of Fekete's Lemma for Subadditive Functions on Cancellative Amenable Semigroups.¶
Ceccherini-Silberstein, T., Coornaert, M., & Krieger, F. (2014). An Analogue of Fekete's Lemma for Subadditive Functions on Cancellative Amenable Semigroups. Journal d'Analyse Mathématique, 59-81.
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Primes¶
- Subadditivity
- … \(a_{m+n}\leq a_m+a_n\), Fekete's lemma identifies a stable asymptotic rate, \(\lim_n a_n/n=\inf_n a_n/n\), and Hammersley and Kingman extend the limiting logic to broader and stochastic subadditive settings. Later semigroup results show that this rate reasoning is not confined to ordinary numerical sequences.
This sourceExtends subadditive-rate reasoning from sequences to semigroup/set-function settings.
- … \(a_{m+n}\leq a_m+a_n\), Fekete's lemma identifies a stable asymptotic rate, \(\lim_n a_n/n=\inf_n a_n/n\), and Hammersley and Kingman extend the limiting logic to broader and stochastic subadditive settings. Later semigroup results show that this rate reasoning is not confined to ordinary numerical sequences.
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