Let DMAP be the class of locally compact groups that admit a (not necessarily continuous) embedding in a compact topological group, and let FIR be the class of locally compact groups all of whose continuous irreducible unitary representations are finite-dimensional. We prove that every almost connected DMAP group is an FIR group.

中文翻译：

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几乎已连接的DMAP组为FIR

假设DMAP是允许在紧凑拓扑组中嵌入（不一定是连续的）的局部紧凑组的类别，而FIR则是其连续不可约的unit表示都是有限维的局部紧凑组的类别。我们证明每个几乎连接的DMAP组都是一个FIR组。