Integral Representation without Additivity
نویسنده
چکیده
Let J be a norm-continuous functional on the space B of bounded E-measurable real valued functions on a set S, where S is an algebra of subsets of S. Define a set function v on £ by : v(E) equals the value of I at the indicator function of E. For each a in B let /0 coo (v(a > a) v(S)) da+ v(a > a) da. -oo Jo Then / = J on B if and only if I(b + c) = 1(b) + 1(c) whenever (b(s) b(t))(c(s) c(t)) > 0 for all s and t in S.
منابع مشابه
On the axiomatization of some classes of discrete universal integrals
Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255–261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001...
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