Les Groupes Libres et Moyannebles
| المؤلف الرئيسي: | Bougoffa, Abdelfattah (Author) |
|---|---|
| مؤلفين آخرين: | Boussaid, Mohamed (Advisor) |
| التاريخ الميلادي: |
2018
|
| موقع: | ورقلة |
| الصفحات: | 1 - 31 |
| رقم MD: | 1161351 |
| نوع المحتوى: | رسائل جامعية |
| اللغة: | الفرنسية |
| الدرجة العلمية: | رسالة ماجستير |
| الجامعة: | جامعة قاصدي مرباح - ورقلة |
| الكلية: | كلية الرياضيات وعلوم المادة |
| الدولة: | الجزائر |
| قواعد المعلومات: | Dissertations |
| مواضيع: | |
| رابط المحتوى: |
عدد مرات التحميل
2
| المستخلص: |
This work includes three chapters: The first chapter concerns some basic notions and definitions of groups as for example that of free group, of equid ecomposability, the action of groups of isometrics on sets. The second: Since we are going to show that there is a measure from the measurement of Lebesgue defined on all R2 to reach, we need the definition of an algebra of Boole, as well as some elementary properties, this is the subject of this chapter. Chapter 2: gives us the tools to build an extension of the measurement of Lebesgue set to R2. In particular to demonstrate the theorem that extends over an algebra of Boole a measure defined on one of his sub-rings. We know that (P (R2), ∩, ∪, C) is a Boolean algebra and that the Lebesgue-measurable sets form a sub-ring of R2 this algebra on which is defined the measure of Lebesgue. The third chapter: deals with: G (2) is a group of automorphisms for which the measure Lebesgue is invariant, hence, if G (2) is amenable, there is an exhaustive measure of R2, G (2) - invariant, finitely additive that extends the measure of Lebesgue. Let’s show that the Group G (2) is amenable. For that we prove, on the one hand, that any commutative group is amenable and, on the other hand, that if N is a normal subgroup of a group G such as N and G/N are amenable, so G is amenable. |
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