Standard representation of multivariate functions on a general probability space
نویسندگان
چکیده
منابع مشابه
Standard Representation of Multivariate Functions on a General Probability Space
It is well-known that a random variable, i.e. a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an extension of this to multivariate functions. This is motivated by some recent constructions of random
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Let (Ω,A, P ) be a probability space, S a metric space, μ a probability measure on the Borel σ-field of S, and Xn : Ω → S an arbitrary map, n = 1, 2, . . .. If μ is tight and Xn converges in distribution to μ (in HoffmannJørgensen’s sense), then X ∼ μ for some S-valued random variable X on (Ω,A, P ). If, in addition, the Xn are measurable and tight, there are S-valued random variables ∼ Xn and ...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2009
ISSN: 1083-589X
DOI: 10.1214/ecp.v14-1477