Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 188--201

WEAK CONVERGENCE OF MASSES ON NORMAL TOPOLOGICAL SPACES

By

BRUNO GIROTTO

And

SILVANO HOLZER, *University of Trieste*

SUMMARY. We obtain some basic results regarding the weak convergence of masses on normal topological spaces, which generalise well known results (e.g the Portmanteau Theorem, the topological interpretation of the weak convergence) related with regular masses on normal spaces. Moreover, we characterise families of masses for which the uniqueness property of the weak limit holds.

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*AMS (1980) subject classification.* 60B10,28A33,28C15,60B05

*Key words and phrases*. Normal topological space, S-integral, mass, weak convergence, $/miu$-regularity, $/miu$-adherence, Levy-topology