# Difference between revisions of "Probability space"

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probability field


1) for all , where and is an arbitrary rearrangement of the numbers ;

2) .

Then there exists a probability measure on the smallest -algebra of subsets of the product with respect to which all the coordinate functions are measurable, such that for any finite subset of and for any -dimensional Borel set the following equation is true:

#### References

 [1] A.N. Kolmogorov, "Foundations of the theory of probability" , Chelsea, reprint (1950) (Translated from Russian) [2] B.V. Gnedenko, A.N. Kolmogorov, "Limit distributions for sums of independent random variables" , Addison-Wesley (1954) (Translated from Russian) [3] J. Neveu, "Mathematical foundations of the calculus of probabilities" , Holden-Day (1965) (Translated from French)

#### References

 [a1] P. Billingsley, "Probability and measure" , Wiley (1979)
How to Cite This Entry:
Probability space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Probability_space&oldid=19753
This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article