On Marcinkiewicz SLLN in Banach Spaces
Korzeniowski, Andrzej
Ann. Probab., Tome 12 (1984) no. 4, p. 279-280 / Harvested from Project Euclid
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Let $S_n = X_1 + \cdots + X_n$ where $(X_n)$ is a sequence of 0-mean i.i.d. random vectors in a $B$-space such that $P(\|X_n\| > t) \leq CP(|X_0| > t)$ for some random variable $X_0 \in L_p$. We show that $S_n/n^{1/p} \rightarrow 0$ in $L_p$ iff $B$ is $p$-stable $(1 \leq p < 2)$.
Publié le : 1984-02-14
Classification:  Marcinkiewicz SLLN,  $p$-stable Banach space,  60B12 
@article{1176993393,
     author = {Korzeniowski, Andrzej},
     title = {On Marcinkiewicz SLLN in Banach Spaces},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 279-280},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993393}
}

Korzeniowski, Andrzej. On Marcinkiewicz SLLN in Banach Spaces. Ann. Probab., Tome 12 (1984) no. 4, pp.  279-280. http://gdmltest.u-ga.fr/item/1176993393/