N^±-integrals and boundary values of Cauchy-type integrals of finite measures

Let Γ be a simple closed Lyapunov contour with finite complex measure ν, and let G⁺ be the bounded and G⁻ the unbounded domains with boundary Γ. Using new notions (so-called N-integration and N⁺- and N⁻-integrals), we prove that the Cauchy-type integrals F⁺(z), z∈G⁺, and F⁻(z), z∈G⁻, of ν are Cauchy N⁺- and N⁻-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the N⁺- and N⁻-integrals play an essential role. Bibliography: 21 titles. (paper)