Abstract
Independence may be considered the single most important concept in probability theory, demarcating the latter from measure theory and fostering an independent development. In the course of this evolution, probability theory has been fortified by its links with the real world, and indeed the definition of independence is the abstract counterpart of a highly intuitive and empirical notion.Independence of random variables{Xi},the definition of which involves the events of σ(Xi),will be shown in Section 2 to concern only the joint distribution functions.
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Chow, Y.S., Teicher, H. (1997). Independence. In: Probability Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1950-7_3
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DOI: https://doi.org/10.1007/978-1-4612-1950-7_3
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