Generalization of weierstrass canonical integrals

In this paper we prove that a subharmonic function in R m of flnite ‚-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of flnite ‚-type which tends to zero uniformly on compacts of R m . The known Brelot-Hadamard representation of subharmonic functions in R m of flnite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of ‚-admissible mass distributions are investigated. c