Integrals of exponential functions with respect to Radon measure

Properties of sets of convergence for integrals of exponential functions in a finite-dimensional Euclidean space are studied in the paper. It is shown that these sets are always convex. In particular, these sets include the sets of absolute convergence of series of exponential functions.
A special class of convex sets is introduced and a complete description of sets of convergence is obtained for the case of open and relatively close convex sets in terms of this class.
Necessary and sufficient conditions for any set of convergence to be open and independently unbounded are formulated.