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The Convergence and Continuity of Set-valued Functions on Fuzzy Measure Space

Author: WuXinLin
Tutor: LiJun
School: Southeast University
Course: Operational Research and Cybernetics
Keywords: Fuzzy Measure Monotone set function Set-valued function Lebesgue theorem Riesz theorem Lusin theorem
CLC: O159
Type: Master's thesis
Year: 2005
Downloads: 56
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Abstract


In this thesis, a closed set valued measurable function on monotone measure space (also known as random sets ) convergence and continuity . Specific work as follows : ( 1 ) the use of several non- additive set function continuity monotone measure space on four types of Lebesgue measurable functions on the closed set value theorem proved . (2) prove that monotone measure space closed set value can be measured on a standard form and function pseudo form of Riesz Theorem . ( 3) limited fuzzy measure space to discuss the convergence of the closed set -valued function in the sense of Hausdorff metric continuity and the set-valued function sequence . Use of the the fuzzy measure zero additive , regularity proved Lusin theorem , the closed set valued measurable functions on fuzzy measure space to establish a link between testability and continuity of set-valued functions . The above result is real-valued measurable functions in fuzzy measure space results further promotion .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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