Law of large numbers in a Banach space
It is well known that the law of large numbers (LLN) holds in its classical form for random variables taking values in a Banach space of type r, \(1\leq r<2\). The author presents sufficient conditions for the LLN to hold in a certain relatively wide class of Banach spaces. This class contains spaces of cotype r, \(1\leq r<2\), in the sense of \textit{D. Kh. Mushtari} [Teor. Veroyatn. Primen. 25, 105-118 (1980; Zbl 0441.60007); English translation in Theory Probab. Appl. 25, 105-117 (1980)] and is defined via some properties of stable distributions.
scientific article; zbMATH DE number 3852098
scientific article