An example in the Weil theory of measurable groups
Abstract: According to a theorem of Andre Weil, if a group possesses an invariant measure which satisfies certain conditions, in particular measurability of the map of , then has a locally bounded Hausdorff topology making a topological group. We offer a simple counterexample to show the need for the above stated condition.
Keywords: Topological group, measurable group, Haar measure, invariant measure, Weil topology
Article copyright: © Copyright 1970 American Mathematical Society