no. 1
On the limiting distribution of non negative additive functions
Compositio Mathematica, Volume 43 (1981) no. 1, pp. 101-105. 
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     author = {Daboussi, H.},
     title = {On the limiting distribution of non negative additive functions},
     journal = {Compositio Mathematica},
     pages = {101--105},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {43},
     number = {1},
     year = {1981},
     zbl = {0458.10037},
     mrnumber = {631429},
     language = {en},
     url = {http://www.numdam.org/item/CM_1981__43_1_101_0/}
}
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Daboussi, H. On the limiting distribution of non negative additive functions. Compositio Mathematica, Volume 43 (1981) no. 1, pp. 101-105. http://www.numdam.org/item/CM_1981__43_1_101_0/

[1] P.D.T.A. Elliott: On the limiting distribution of f (p + 1) for non negative additive functions. Acta Arithmetica XXV (1974) 259-264. | MR | Zbl

[2] P. Erdös and A. Wintner: Additive arithmetical functions and statistical independence. Amer. J. Math. 61 (1939) 713-721. | JFM | MR | Zbl

[3] I. Kátai: On the distribution of arithmetical functions on the set of primes plus one. Compositio Math. 19 (1968) 278-289. | Numdam | MR | Zbl