We have been working on the formalization of the probability and the randomness. In [15] and [16], we formalized some theorems concerning the real-valued random variables and the product of two probability spaces. In this article, we present the generalized formalization of [15] and [16]. First, we formalize the random variables of arbitrary set and prove the equivalence between random variable on Σ, Borel sets and a real-valued random variable on Σ. Next, we formalize the product of countably infinite probability spaces.
@article{bwmeta1.element.doi-10_2478_forma-2013-0003,
author = {Hiroyuki Okazaki and Yasunari Shidama},
title = {Random Variables and Product of Probability Spaces},
journal = {Formalized Mathematics},
volume = {21},
year = {2013},
pages = {33-39},
zbl = {1281.60006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0003}
}
Hiroyuki Okazaki; Yasunari Shidama. Random Variables and Product of Probability Spaces. Formalized Mathematics, Tome 21 (2013) pp. 33-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0003/
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