Browsing FACULTY OF NATURAL & APPLIED SCIENCES by Subject "Measure theory"

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The area formula for the Hausdorff measure

Nghaywi, Vanessa Pierre (Notre Dame University-Louaize, 2018-06-27)

In this thesis, we will prove a very important theorem in real analysis called The Area formula for the Hausdorff Measure. This theorem is an extension of the well known theorem the Change of variables formula for the Lebesgue measure. In this thesis, we will define the Hausdorff measure and prove some of its properties. We will also define Lipschitz functions and prove some of its properties also. Then, we continue the thesis by proving all the lemmas needed to finalize the proof of the Area formula for the Hausdorff measure. Finally, we finish this thesis by showing three applications of the ...
Fuzzy measure spaces and fuzzy integrals: an overview and an application

Mahmoud, Faten (Notre Dame University-Louaize, 2021)

Fuzzy measure theory is a generalization of classical measure theory. It was first introduced by Lotfi Zadeh in 1965 in his famous paper ”Fuzzy Sets”. After more than 50 years of the existence and development of classical measure theory, mathematicians felt that the additivity property is, in some applications, too restrictive. It is also unrealistic under real and physical conditions where measurement errors are unavoidable. According to Sugeno, fuzzy measures are obtained by replacing the additivity condition of classical measures with weaker conditions of monotonicity and continuity. Chapter ...

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