Generated Measures And Integratıon

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2016

Student: ÇETİN CEMAL ÖZEKEN

Supervisor: CÜNEYT ÇEVİK

Abstract:

In this study, systems called α-arithmetic, which are building blocks of non-Newtonian calculus were investigated in a deep perspective and enriched with examples. Generated measure and generated outer meusere were defined, and also some properties were mentioned. Generated Lebesgue measure was defined. The concept of integrability was scrutinized. Besides, Levi's Theorem, Fatou's Lemma and the Lebesgue Dominated Convergence Theorem, which has an important role in integral theory, were interpreted according to these new integrals. Furthermore, generated Riemann integral was defined and finally the relation between generated Riemann integral and generated Lebesgue integral was examined.