${{\mathcal{P}}_{mcv}}$-measure and ${{\mathcal{P}}_{mcv}}$-capacity

In this work, introduces important objects of the theory of $m$-convex $\left( m-cv \right)$ functions, $mcv$-polar sets, ${{\mathcal{P}}_{mcv}}$-measures $\omega *(x,E,D)$, $mcv$-capacity quantities $\text{ }{{\mathcal{P}}_{mcv}}(E,D)=-\int\limits_{D}{\omega *(x,E,D)dV}$ and the capacity of the condenser $C\left( E,D \right)$ 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.