Abstract
Abstract Following the paper of Pkhakadze [Trudy Tbiliss. Mat. Inst. Razmadze 20: 167–209, 1954], we consider some properties of real-valued functions of two variables, which are not assumed to be measurable with respect to the two-dimensional Lebesgue measure on the plane 𝐑2, but for which the corresponding iterated integrals exist and are equal to each other. Close connections of these properties with certain set-theoretical axioms are emphasized.
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