Linear Approximations In Convex Metric Spaces And The Application In The Mixture Theory Of Probability Theory

The average of a family of probability distribution functions (in short, distribution function) by a distribution function, as weight function, is also a distribution function. This average is said to be the mixture of the family of distribution functions by the weight function. What are the conditions for the existence of a weight function? If such a weight function exists, what is that function? These problems are said to be the problems of linear approximability, or decomposability for distribution functions. Questions concerning this topic have been raised long ago. Only ad hoc procedures have been found. General methods for these problems have not been worked out. In this book, the author deals with the treatment of such general method.