الدوال المستمرة المطلقة والمقيدة التغاير == On Absolutely Continuous and of Bounded Variation Functions
Author name:
نور رياض اديب كريم
Supervisor name:
راضي ابراهيم محمد علي
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Baghdad
Language:
English
University location:
Baghdad
First pages:
27T1016 - p.pdf
Abstract:
The main aim of this thesis is to give two strong forms of real - valued functions defined on closed, bounded interval [a,b] with respect to Lebesgue partitions instead of Riemann partitions. These strong forms are called "Lebesgue bounded variation" real - valued functions on [a,b] and "Lebesgue absolutely continuous" real - valued functions on [a,b]; the relationship between Lebesgue absolutely continuous real - valued functions on [a,b] and Lebesgue bounded variation real - valued functions on [a,b] are also studied. Moreover, the relationship between of bounded variation real - valued functions on [a,b] and Lebesgue bounded variation real - valued function on [a,b] has been funded. We also find the relationship between absolutely continuous real - valued functions on [a,b] and Lebesgue absolutely continuous real - valued functions on [a,b]. Furthermore, Algebraic properties of Lebesgue bounded variation real - valued functions on [a,b] and algebraic properties of Lebesgue absolutely continuous real - valued functions on [a,b] have been studied. Then some results and theorems dealing with Lebesgue bounded variation real - valued functions on [a,b] and Lebesgue absolutely continuous real - valued functions on [a,b] is concluded. Finally, we study normed space of Lebesgue bounded variation real - valued functions on [a,b] and normed space of Lebesgue absolutely continuous real - valued function on [a,b].
