Mean values and Banach limits

Ralph A. Raimi
1957 Proceedings of the American Mathematical Society  
For certain bounded real valued functions on the real line, lim" (1/2 a)flafix+t)dt exists uniformly in x, and is a constant, w(/). On the space of such functions, the limit m(f) is a translation-invariant positive functional of norm one, and hence generalizes the notion \im\x\^xf(x). For bounded sequences, such a func-
doi:10.1090/s0002-9939-1957-0102008-7 fatcat:twijtfl4ynfblna7u4l5tbwprq