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$%J. Ferrera, Mosco convergence of sequences of homogeneous polynomials, Rev. Mat. Complut. 11 (1998), no. 1, 31–41.%$

In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences.

1991 Mathematics Subject Classification: Primary: 46E25; secondary: 12E05.