This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
The assertion that "Every topological group can be taken as a measurable group" is false. The problem is that if are the Borel sets for and are the Borel sets for , it does not necessarily occur that .
Thus, the continuity of the group operations is not enough to ensure the measurability of certain sets. If, however, the group has a countable basis, it is true that and then the statement becomes true.