منابع مشابه
Random Measurable Selections
We make the first steps towards showing a general “randomness for free” theorem for stochastic automata. The goal of such theorems is to replace randomized schedulers by averages of pure schedulers. Here, we explore the case of measurable multifunctions and their measurable selections. This involves constructing probability measures on the measurable space of measurable selections of a given me...
متن کاملBore1 measurable selections of Paretian utility functions
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] i...
متن کاملApproximations of upper and lower probabilities by measurable selections
A random set can be regarded as the result of the imprecise observation of a random variable. Following this interpretation, we study to which extent the upper and lower probabilities induced by the random set keep all the information about the values of the probability distribution of the random variable. We link this problem to the existence of selectors of a multi-valued mapping and with the...
متن کاملEvaluation and optimization of complex object selections
We provide a general framework for declarative selection operations for complex object databases based on the safe calculus for complex objects Within this framework we consider a class of single pass evaluable selection operations We show how such selection operations can be succinctly expressed by programs that use only very simple positive existential selections Also a syntactic criterion is...
متن کاملIntegral of Complex-Valued Measurable Function
In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valu...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1995
ISSN: 0263-6115
DOI: 10.1017/s144678870003826x