On the strong law of large numbers for non-independent B-valued random variables. (English) Zbl 1063.60004
Summary: This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jørgensen and Pisier theorem are obtained.
MSC:
| 60B12 | Limit theorems for vector-valued random variables (infinite-dimensional case) |
| 60F15 | Strong limit theorems |
Keywords:
strong law of large numbers; Banach space valued random variable sequence; \(p\)-smoothable Banach spaceReferences:
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