The basic aim of this thesis is to extend the definition of an n-dimensional vector measure so as to allow it to assume infinite values. In the 1-dimensional case, when one extends the notion of a non-negative measure to that of a signed measure which may assume negative values, it is necessary to assume that the signed measure takes on at most one of the values (+ oo) or(- oe). In a similar fashion it is shown that in arder to successfully extend the definition of a finite-valued n-dimensional measure, it is necessary to suppose that the extended measure assumes at most one infinite value. [...]

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