Criteria for the strong law of large numbers for sequences of arbitrary random vectors

✍ Scribed by N. Etemadi

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 341 KB
• Volume: 33
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00123-x

✦ Synopsis

In the following note we obtain sufficient conditions so that the strong law of large numbers would hold for an arbitrary sequence of random variables taking values in a separable Banach space. The conditions are sharp in the sense that they imply the strong law for 2-exchangeable random vectors and they become necessary when the random vectors are pairwise independent, identically distributed.