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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).
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Haar measure on a quotient, References for
I personally had this issue and couldn't get my head around on some of the basic steps one sees in literature on $ L$-functions. My personal favourites are
Deitmar & Echterhoff: Principles of Harmoni …