A Criterion of Standardness
Standardness of a given probability space is equivalent to a certain property of a measurable map from to a measurable space Interestingly, the answer (standard, or not) does not depend on the choice of and . This fact is quite useful; one may adapt the choice of and to the given No need to examine all cases. It may be convenient to examine a random variable a random vector a random sequence or a sequence of events treated as a sequence of two-valued random variables,
Two conditions will be imposed on (to be injective, and generating). Below it is assumed that such is given. The question of its existence will be addressed afterwards.
The probability space is assumed to be complete (otherwise it cannot be standard).
Read more about this topic: Standard Probability Space
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“If we are to take for the criterion of truth the majority of suffrages, they ought to be gotten from those philosophic and patriotic citizens who cultivate their reason.”
—James Madison (1751–1836)