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By Christoph Klein

This ebook reviews a wide economic system. It offers with a static microeconomic version of an alternate marketplace with natural pageant. rather than the sigma-additive concept, the finitely additive concept, the final Jordan content material and the overall Riemann integration are used respectively. via a really expert chance version, the writer obtains an exact interpretation strictly according to microeconomic tools of size. specifically, the that means of an agent and of a coalition is defined and the Core-Walras equivalence is deduced. the writer elaborates an straightforward illustration via damaged non-stop services and the classical Riemann quintessential. A conjecture in regards to the relief of the dynamical case onto generalized differential equations is extra.

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The space pxm~ was endowed with the metric oxll closed convergence metric on P and where II II II where 0 was the was the Euclidean metric on m~. On C (Stone (Ro) ,pxm~) we considered the sup metric do defined by II I xES tone (Ro) } where n obtain e (Stone (Ro) ,pxm+) doe @,f)=do(Exe,Fxf) :=sup{o (E(x) ,F(x»+ lIe(x)-f(x) - n l:, t EC (Stone (Ro) ,pxm+). Due to prop. II. 5 we as the completion of the extended, replicated endowment mappings with respect to the sup metric do. A continuous mapping defined on a compact space is uniformly continuous.

The set N of agents is a countable, dense subset of Stone (BG(~)}. In the sequel we will recognize that supp(v) has no isolated point provided that pure competition holds. e. ~: is v-uniformly distributed in Stone(BG(~». AEBG(~) - then X(cl(A» is a cbntinuous function on Stone(BG(~». e. equivalently on N or on Stone(BG(~». Therefore the above stated requirement on our observation model is fulfilled. Observe the following interp~etation of (i): If ~ is chosen by random, then ~ yields a v-uniformly distributed sequence with probability one.

The prop. 7 (i) holds analogously if lRn is replaced by a compact metric space. Since prop. 7 (i) is a finitely additive result, formulated in the o-additive language, it cannot be applied directly with respect to a dense subset S of K. A different, equivalent characterization allows that treatment. We noted prop. 7 (i) mainly to emphasis the similarity between the classical and the generalized theory. Due to our introductory explanations we are mainly interested in a calculus of equivalence classes suitable fo~ our purposes.

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