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AbstractLet T be a finite set for which card T is a natural nonstandard number. The linear space ${ℂ}^T$ of complex-valued functions on T is nonstandard. For the analysis on ${ℂ}^T$ we need a concept of nearstandardness in this space. A version how to introduce such a concept is proposed. Some elementary examples are given. CONTENTSIntroduction.................................................................................................................50. Preliminary notes....................................................................................................7 0.1....