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Full-Text Articles in Mathematics
On The Basic Representation Theorem For Convex Domination Of Measures, J. Elton, Theodore P. Hill
On The Basic Representation Theorem For Convex Domination Of Measures, J. Elton, Theodore P. Hill
Research Scholars in Residence
A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case (purely atomic measures with a finite number of atoms), and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-dimensional case follows quickly from the finite-dimensional case with the use of the approximation property.
Constructions Of Random Distributions Via Sequential Barycenters, Theodore P. Hill, Michael Monticino
Constructions Of Random Distributions Via Sequential Barycenters, Theodore P. Hill, Michael Monticino
Research Scholars in Residence
This article introduces and develops a constructive method for generating random probability measures with a prescribed mean or distribution of the means. The method involves sequentially generating an array of barycenters which uniquely defines a probability measure. Basic properties of the generated measures are presented, including conditions under which almost all the generated measures are continuous or almost all are purely discrete or almost all have finite support. Applications are given to models for average-optimal control problems and to experimental approximation of universal constants.