Geodesic
Density functions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 4, pp. 387-414 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study properties of $\rho$-semiadditive functions, $N(\alpha+\beta)\leq N(\alpha)+(1+\alpha)^\rho N\left(\frac\beta{1+\alpha}\right)$. Their theory is similiar to the very investigated one of semiadditive functions. The functions of density $N(\alpha)$=$\limsup r^{-\rho}(f(r+\alpha r)-f(r))$ $(r\to\infty)$ are $\rho$-semiadditive. One of results of the note is an extension of the theorem of Polya (1929) on existence of maximal and minimal densities. We are interested in the question of uniformity in the above limiting relation. 
@article{JMAG_2000_7_4_a2,
     author = {A. F. Grishin and T. I. Malyutina},
     title = {Density functions},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {387--414},
     year = {2000},
     volume = {7},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_4_a2/}
}
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A. F. Grishin; T. I. Malyutina. Density functions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 4, pp. 387-414. http://geodesic.mathdoc.fr/item/JMAG_2000_7_4_a2/