The Dubovickii-Miljutin Lemma and characterizations of optimal allocations in non-smooth economies

Article Abstract:

An optimization problem in the form of the Dubovickii-Miljutin Lemma is discussed. This lemma is used to formulate optimality properties in a non-smooth economy. Results of the strengthening of the lemma provide insights into other applications such as determining the optimization conditions in an economy characterized by non-convexity or one which is influenced by externalities.

Research, Mathematical optimization, Optimization theory

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The Debreu Gap Lemma and some generalizations

Article Abstract:

The Debreu Gap Lemma and its generalizations to totally ordered sets are discussed. The importance of studying utility functions in economics is examined. A theory of continuity of generalized utility functions is proposed.

Europe, Utility theory, Utility functions, Global economy

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Induced families of choice probabilities

Article Abstract:

A thoroughgoing discussion of the concept of induced probability is presented. Path rule, Caratheodory extension, etc. are discussed.

United Kingdom, Probabilities, Probability theory, Mathematical analysis

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