ON THE EXTENSION OF SCHWARTZ DISTRIBUTIONSTO THE SPACE OF DISCONTINUOUSTEST FUNCTIONS OF SEVERAL VARIABLES

摘要

The present paper is devoted to the inves-tigation of the properties of the space of distributions with discontinuous test functions of several variables. The consid-eration of discontinuous test functions allows us to define the operations of integration of distributions and multiplication of distributions by discontinuous functions which are continu-ous, defined everywhere and coinciding with the ordinary ones for regular distributions. These operations are undefined in the classical space D of distributions with continuous test functions, yet necessary in many applications of distribution theory: in what follows, we consider a class of zero-sum games with discontinuous payoff functions; these games may have no solution in the set of pure strategies or in the set of classical mixed strategies, but may possess the solution in the set of 7Z'-mixed strategies which are the elements of the new space of distributions.