Utility representations of preferences: some results : delo diplomskega seminarja
Tominc, Julija (Author), Bosi, Gianni (Mentor) More about this mentor... This link opens in a new window, Košir, Tomaž (Mentor) More about this mentor... This link opens in a new window

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The thesis presents some classical results concerning the Utility Theory. We present the requirements that a preorder must satisfy in order to be representable with a utility function while also exploring weaker conditions such as in the case of quasi-preorders. We establish the existence of a utility function, and explore the requirements for its upper semi-continuity in the form of the Rader theorem. Further using the Uryshon-Nachbin approach we present the proofs for both the classical Debreu theorem and the Eilenberg theorem, guaranteeing us the existence of a continuous utility on second countable topological spaces and connected separable topological spaces, respectively.

Keywords:utility function, continuity, Nachbin-Uryshon approach, Debreu separability
Work type:Final seminar paper (mb14)
Tipology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
COBISS.SI-ID:18479449 This link opens in a new window
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Secondary language

Title:Funkcija koristnosti in preference: nekaj rezultatov
Delo diplomskega seminarja predstavi nekaj klasičnih rezultatov teorije koristnosti začenši z zahtevami za obstoj funkcije koristnost za totalne binarne relacije. Dodatno predstavimo šibkejše zahteve, ki zadostujejo za obstoj funkcije koristnosti za binarne relacije, ki niso tranzitivne. Nadaljujemo z raziskovanjem zahtev za zveznost funkcije koristnosti na 2-števnem topološkem prostoru v obliki Debreujevega izreka in obstoja zvezne funkcije na povezanem in separabilnem topološkem prostoru, ki je predstavljen z Eilenbergovim izrekom. Izreka dokažemo s pomočjo Nachbinove razširitve Uryshonovega dela.

Keywords:funkcija koristnosti, Nachbin-Uryshon, zveznost, Debreujeva ločljivost

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