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الدوال المستمرة المطلقة والمقيدة التغاير == On Absolutely Continuous and of Bounded Variation Functions
اسم المؤلف:
نور رياض اديب كريم
اسم المشرف:
راضي ابراهيم محمد علي
الموضوع العام:
علوم الرياضيات
السنة:
2016
الموضوع الدقيق:
الرياضيات
الدرجة:
ماجستير
الجامعة:
جامعة بغداد
اللغة:
الانكليزية
مكان الجامعة:
بغداد
الصفحات الاولى:
📎 27T1016 - p.pdf
المستخلص:
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].
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