Abstract
The present chapter provides a quick reference to the probabilistic facts that are often used throughout the book. For more detailed treatment of these topics readers may consult the commentaries to this chapter and the works cited therein. The most statements below are given for granted and only a few of them that cannot be found easily in the literature are equipped with proofs. The topics reviewed are not related to each other directly. Because of this, readers may skip this chapter and return to it when necessary. For the purposes of this book, it is quite sufficient to assume that the r.v.’s under consideration take their values in a complete separable metric space. We assume this throughout the book without additional commentaries. Moreover, typically we restrict ourselves with real or vector-valued r.v.’s.
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References
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Kalashnikov, V. (1997). Miscellaneous Probability Topics. In: Geometric Sums: Bounds for Rare Events with Applications. Mathematics and Its Applications, vol 413. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1693-2_2
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