${{\mathcal{P}}_{mcv}}$-measure and ${{\mathcal{P}}_{mcv}}$-capacity in the class of $m$-convex functions

In this work, we introduce important objects of the theory of $m$-convex $(m-cv)$-functions, $mcv$-polar sets, ${{\mathcal{P}}_{mcv}}$-measures $\omega *(x,E,D)$, $mcv$-capacity quantities ${{\mathcal{P}}_{mcv}}(E,D)=-\int\limits_{D}{\omega *(x,E,D)dV}$ and the capacity of the condenser $C(E,D)$ in the class of $m$-convex functions. Similarly to harmonic measures in classical potential theory, ${{\mathcal{P}}_{mcv}}$-measures have the property of extremality in the class of $m$-convex functions.