Lebesgue Measurability of Continuous Functions in Constructive Analysis<br/>

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Lebesgue Measurability of Continuous Functions in Constructive Analysis

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55586 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ardeshir, Mohammad
Abstract:
The thesis opens with a discussion of the distinction between some of the classical and the constructive notions in mathematical analysis. There then follows a description of the three main varieties of modern constructive mathematics: Bishop’s constructive mathematics, the recursive constructive mathematics of the Russian School, and Brouwer’s intuitionistic mathematics. The main purpose of the thesis is to prove the independence, relative to Bishop’s constructive mathematics, of each of the following statements:There exists a bounded, point-wise continuous map of [0, 1] into R that is not Lebesgue measurable.If µis a positive measure on a locally compact space, then every real-valued map denned on a full set is measurable with respect to µ.
Keywords:
Intuitionism ; Bishop's Constructive Mathematics ; Constractive Analysis ; Lebesgue Spaces ; Lebesgue Measurability

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