Abstract
As indicated before, we consider only certain highlights of measure theory in probability spaces. First we clarify the arithmetic of the extended real line \(\bar{R}\): all real numbers and the two ideal points +∞, -∞. The introduction of these ideal points is for the mathematical convenience that every set of real numbers have a sup (least upper bound) and an inf (greatest lower bound); these will be pursued in lesson 7. On the other hand, the probability side, there is the real Galton-Watson process wherein we just might have positive probability that the time to extinction is infinite; the earliest example of this is the computation of the probabilities that the lineage of a certain British peer should die out.
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© 1989 Springer Science+Business Media New York
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Nguyen, H.T., Rogers, G.S. (1989). Some Algebra of Random Variables. In: Fundamentals of Mathematical Statistics. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1013-9_27
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DOI: https://doi.org/10.1007/978-1-4612-1013-9_27
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6984-7
Online ISBN: 978-1-4612-1013-9
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