own. Potential theory His contributions to potential theory are very important. The results of his paper occupy paragraph 24 of chapter II of the textbook , as remarked by in . Also, his researches and on the asymptotic behaviour of the electric field near singular points of the conducting surface, widely known among the specialists (as several works of V.G. Maz'ya, S.A. Nazarov, B.A. Plamenevsky, B.W. Schulze and others testify) can be included in between his works in potential theory. Measure and integration theory His main contributions to those topics and are the papers and . In the first one he proves that a condition on a sequence of integrable functions previously introduced by Mauro Picone is both necessary and sufficient in order to assure that limit process and the integration process commute, both in bounded and unbounded domains: the theorem is similar in spirit to the dominated convergence theorem, which however only states a sufficient condition. The second paper contains an extension of the Lebesgue's decomposition theorem to finitely additive measures: this extension required him to generalize the Radon–Nikodym derivative, requiring it to be a set function belonging to a given class and minimizing a particular functional. Complex analysis of functions of one and several variables He contributed to both the classical topic of complex analysis in one variable and the more recent one of complex analysis in several variables. His contributions to complex analysis in one variable are essentially approximation results, well described in the survey paper . In the field of functions of several complex variables, his contributions were outstanding, but also not generally acknowledged. Precisely, in the paper he solved the Dirichlet problem for holomorphic function of several variables under the hypothesis that the boundary of the domain has a Hölder continuous normal vector (i.e. it belongs to the class) and the Dirichlet boundary condition is a function belonging to the Sobolev space satisfying the weak form of the tangential Cauchy–Riemann condition, extending a previous result of Francesco Severi: this theorem and the Lewy–Kneser theorem on the local Cauchy problem for holomorphic functions of several variables, laid the foundations of the theory of CR-functions. Another important result is his proof in of an extension of Morera's theorem to functions of several complex variables, under the hypothesis that the given function is only locally integrable: previous proofs under more restrictive assumptions were given by Francesco Severi in