Bore1 measurable selections of Paretian utility functions
نویسندگان
چکیده
We show that there is a Bore1 measurable selection of Paretian utilities in ‘markets with a continuum of traders’. Theorem: Let T and X be Polish spaces, R a Bore1 subset of T x X xX, and B={(t,x): (t,x,x)ER}. Suppose that for each t, R,={(x,y): (t,x,y)ER} is a preference order on B, = {x: (t,x) EB). Then there is a Bore1 measurable function f: B-$0, l] such that for all t E IT; f,: B,+[O, I] is a Paretian utility or continuous representation of R,. This improves earlier results showing that there are universally measurable f.
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تاریخ انتشار 1993