Strong laws of large numbers in certain linear spaces
Annales de l'Institut Fourier, Volume 24 (1974) no. 2, p. 205-223

In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous F-norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.

Dans cet article, on explore la convergence presque sûre des séries de variables aléatoires prenant leurs valeurs dans l’espace métrique linéaire et les lois fortes des grands nombres pour suites de vecteurs aléatoires. Dans la partie 2, on considère le cas de l’espace de Banach où les résultats dépendent de la géométrie de la boule unité. Dans la partie 3, on étudie les vecteurs aléatoires dans un espace possédant une norme non-nécessairement homogène ; la partie 4 est consacrée aux suites de vecteurs indépendants et équidistribués.

@article{AIF_1974__24_2_205_0,
     author = {Woyczynski, Wojbor A.},
     title = {Strong laws of large numbers in certain linear spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {24},
     number = {2},
     year = {1974},
     pages = {205-223},
     doi = {10.5802/aif.514},
     zbl = {0275.60039},
     mrnumber = {53 \#9318},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1974__24_2_205_0}
}
Woyczynski, Wojbor A. Strong laws of large numbers in certain linear spaces. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 205-223. doi : 10.5802/aif.514. http://www.numdam.org/item/AIF_1974__24_2_205_0/

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