A comparison theorem for the law of large numbers in Banach spaces

Deli Li, Han-Ying Liang

Let $(\mathbf{B},\Vert \cdot \Vert )$ be a real separable Banach space. Let $\{X,X_n;n\ge 1\}$ be a sequence of i.i.d. {\bf B}-valued random variables and set $S_{n} = \sum_{i=1}^{n}…