Feynman integral for exponential interaction in four-dimensional space-time. I

By means of the change of variables $\varphi(x)\to{:}\exp\varphi(x){:}_{1+3}+\text{ counterterms}$ a countably additive measure is constructed on the space of Gel'fand–Shilov–Jaffe generalized functions, and it is used to obtain an integral representation for the Green's functions of quantum field theory with the interaction ${:}\exp\varphi{:}_{1+3}$ without ultraviolet cutoff (and with a space-time cutoff).