Orthogonal properties of independent functions

This paper investigates the orthogonal structure of independent systems of functions. The tendency in dealing with independent functions has been largely to establish results relating to the law of large numbers and central limit theorems (see [1ii) ('). The treatment here is concerned with an analytical study of the orthogonal properties of independent functions and does not consider probability interpretations. Two functions f1(t) and f2(t) are said to be independent over the interval (0, 1), if for any ai, f3 (i= 1, 2) we have