P-MEASURE IN THE CLASS OF m-CONVEX FUNCTIONB

This paper investigates key objects within the theory of -convex functions, specifically focusing on -polar sets, -measures, and capacitive values. Drawing analogies to harmonic measures in classical potential theory, the author establishes that -measures exhibit extreme properties within the class of -convex functions. The work characterizes the properties of -polar sets, outlining their relation to Lebesgue and Hausdorff measures. Based on the Trudinger-Wang theorem, the existence criteria for these sets are examined under the conditions and . Furthermore, the concept of -capacity for a condenser is introduced, and its fundamental properties – such as monotonicity, countable subadditivity.