On the representation of nonseparable analytic sets

Recently, the author considered extending the concepts of a Borel and analytic set for nonseparable metric spaces by allowing $\sigma$-discrete families to replace countable families in the classical definitions. The resulting class of ``extended Borel sets'' was shown to lead to a new class of sets, intermediate to the Borel and analytic sets. In the present paper we show that the corresponding class of ``extended analytic sets'' does not lead to a new class of sets but actually coincides with the standard class of analytic sets. Thus their importance lies in the fact that they provide a useful ``representation'' for the analytic sets in arbitrary spaces. Several such representations are shown to lead to the same class of analytic sets.