The Steinhaus theorem and regular variation: de Bruijn and after (Q740459)

There are several purposes of this paper. The authors briefly recall the history of the theory of regular variation, including de Bruijn's contributions, and discuss recent developments in this area. Further, they introduce slow variation of functions \(h:X\to X\), where \(X=L_1(G)\), \(G\) being a (separable) locally compact metric group with Haar measure. The uniform convergence theorem for such functions is proved.