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Cohn himself recommends historical notes at the end of sections 15, 16 of Abstract Harmonic Analysis by Hewitt and Ross, volume 1. Here is an excerpt: "Invariant integration on one or another special class of groups has long been known and used. A detailed computation of the invariant integral on $\mathfrak{SD}(n)$ was given in 1897 by HURWITZ [1]. ...

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A good source for these types of questions is Miller's site Earliest Known Uses of Some of the Words of Mathematics. On the norms in vector spaces we find the following: "On page 57 of his 1908 paper “Über die Auflösung linearer Gleichungen mit unendlich vielen Unbekannten,” Rendiconti del Circolo Matematico di Palermo, 25 (1908), Erhard Schmidt defines ...

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Try these references: Section 7.5 of History of Topology, edited by I. M. James. Section 2.2 of the chapter "Topological Features of Topological Groups" in Handbook of the History of General Topology, volume 3, edited by C.E. All and R. Lowen

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