An integral criterion for $m-sh$-functions

It is well-known that subharmonic functions are defined by integral mean value, i.e. mean value over the sphere (ball) of the function at the neighbourhood of the point is greater or equal to the value of the function at this point.
Plurisubharmonic and $m$-subharmonic functions are defined by using subharmonicity at complex lines and $m$-dimensional complex planes, respectively. In this talk we introduce a new integral criterion for $m-sh$-functions. It can be used like subharmonic functions as a definition for $m-sh$-functions. In particular the obtained results can be applied for plurisubharmonic functions.