We consider representations of scalar and vector random functions on a set T in the form of infinite or finite sums with terms, which are scalar functions on T with random coefficients, under rather general assumptions on the set T and properties of random functions. In particular, the cases are investigated when T is a compact topological space, measurable space with positive measure. In Part I the Karhunen-Loeve type representations are considered. More general representations are studied in Part II.
