# Random Variables and Product of Probability Spaces

Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2013)

- Volume: 21, Issue: 1, page 33-39
- ISSN: 1426-2630

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topHiroyuki Okazaki, and Yasunari Shidama. "Random Variables and Product of Probability Spaces." Formalized Mathematics 21.1 (2013): 33-39. <http://eudml.org/doc/267275>.

@article{HiroyukiOkazaki2013,

abstract = {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.},

author = {Hiroyuki Okazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

language = {eng},

number = {1},

pages = {33-39},

title = {Random Variables and Product of Probability Spaces},

url = {http://eudml.org/doc/267275},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Hiroyuki Okazaki

AU - Yasunari Shidama

TI - Random Variables and Product of Probability Spaces

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 1

SP - 33

EP - 39

AB - 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.

LA - eng

UR - http://eudml.org/doc/267275

ER -

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