摘要
Let F_1,...,F_N be 1-dimensional probability distribution functions and C be an N-copula. Define an N-dimensional probability distribution function G by G(x_1,...,x_N)=C(F_1(x_1),...,F_N(x_N)). Let ν, be the probability measure induced on R^N by G and μ be the probability measure induced on [0,1]^N by C. We construct a certain transformation Φ of subsets of R^N to subsets of [0, 1]^N which we call the Fréchet transform and prove that it is measure-preserving. It is intended that this transform be used as a tool to study the types of dependence which can exist between pairs or N-tuples of random variables, but no applications are presented in this paper.
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