finitely additive set function

finitely additive set function

[¦fī‚nīt·lē ¦ad·ə·div ′set ‚fəŋk·shən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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in [0,1], then [parallel] [f.sub.n] [[parallel].sub.p] [right arrow] 0 for n [right arrow] [infinity]), the finitely additive set function [M.sub.p] : B [right arrow] [L.sup.p] defined by
It is worth noting that a purely finitely additive set function [Phi] on the field of subsets of the integers (Z, [Sigma]) cannot be represented by a sequence of real numbers in the sense that there exists no sequence of positive real numbers, [Lambda] = {[[Lambda].sub.n]} which defines [Phi], that is, there is for no [Lambda] such that
For example the lim inf: [l.sub.[infinity]] [approaches] R, defines a purely finitely additive set function on the integers which is not representable by a sequence of real numbers.