Lower types of δ-subharmonic functions of the nonintegral order - Zabolotsky , M. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
It is proved that the lower types of functions T (r, u) and N (r, u) = N (r, u_1) - N (z, u_2) relative to the proximate order ρ(r) of a function u=u_1-u_2 of fractional order ρ δ-subharmonic in R^m, m≥2, coincide, that is, are simultaneously minimal or mean. In the case of an arbitrary proximate order ρ(r) the assertion is, in general, false.