Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in advance (as for instance for multivariate Bernoulli distributions), a single suitably chosen projection determines the distribution. Several applications of these results are considered.

翻译：利用Heppes关于有限支撑离散概率测度定理的一些推广，我们解决了基于投影的分类与检验问题。特别地，当分布的支撑预先已知时（例如多元伯努利分布），单个合适选取的投影即可确定该分布。本文讨论了这些结果的若干应用。