Arrow and Debreu proved that, if in the mathematical model of the economy that they defined some conditions are satisfied, then there is a price system under which there is Walras equilibrium in this economy. We examine a procedure, defined on the basis of a continuous mapping, of transformation of production sets of the Arrow-Debreu economies in which at least one of the assumptions concerning the production sets is not satisfied. Finally, we get a class of ArrowDebreu economies in which, after modification, there is Walras equilibrium. The research methods are based on the analysis of the linear mappings in real vector space of finite dimension, and the results have the form of mathematical theorems.