Let and be locally compact groups with fixed two-sided invariant Haar measures. A polyhomomorphism is a closed subgroup with fixed Haar measure, whose marginals on and are dominated by the Haar measures on and . A polyhomomorphism can be regarded as a multi-valued map sending points to sets equipped with ‘uniform’ measures. For two polyhomomorphisms and there is a well-defined product . The set of polyhomomorphisms is a metrizable compact space with respect to the Chabauty-Bourbaki topology and the product is separately continuous. A polyhomomorphism determines a canonical operator , which is a partial isometry up to a scalar factor. For example, we consider locally compact linear spaces over finite fields and examine the closures of groups of linear operators in semigroups of polyhomomorphisms.

Bibliography: 40 titles.

让和成为具有固定两侧不变 Haar 测度的局部紧群。一个polyhomomorphism是一个封闭的亚组固定哈尔措施，其边缘人在与由哈尔措施对被支配和。多同态可以被看作是一个多值映射，将点发送到配备“统一”度量的集合。对于两个多同态，有一个明确定义的乘积。多同态集是一个关于 Chabauty-Bourbaki 拓扑的可度量紧空间，并且乘积是单独连续的。多同态确定规范算子，这是达到标量因子的部分等距。例如，我们考虑有限域上的局部紧致线性空间，并检查多同态半群中线性算子群的闭包。

参考书目：40 个标题。