Abstract
In this lesson, we take a fixed probability space [ΩSP] with events A,B, … and rephrase the properties of integration of random variables (measurable functions X, Y, Z, X1X2…) in terms of the following definition; now “almost everywhere (a.e.)” is “almost surely (a.s.)”. Only a few proofs are included, the details of lesson 10 not withstanding. Some results are obvious or at least like those in “sophomore calculus”; others involve substantially more theory. Since some writers restrict “expected value” to finite cases, the reader may notice small differences in phraseology.
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© 1989 Springer Science+Business Media New York
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Nguyen, H.T., Rogers, G.S. (1989). Theorems for Expectation. In: Fundamentals of Mathematical Statistics. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1013-9_32
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DOI: https://doi.org/10.1007/978-1-4612-1013-9_32
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6984-7
Online ISBN: 978-1-4612-1013-9
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