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Mean values and Banach limits
1957
Proceedings of the American Mathematical Society
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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