Abstract
Let be a probability measure on a finite set I , with I as a support. Let be a reai function on I. The aim of this article is to prove that we can express such a function as a sum of non constants functions orthogonal with respect to the inner product considered as the integral, of the product of two functions, with respect to the probability measure. This result can easily be generalized to the finite product of finite sets on which a product probability measure is defined. From this deoomposition an exact partition of X 2 on multi way contingency tables is easily proved.
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