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On a New Kind of Collection of Subsets Noted by

Author: Hassan H. Ebrahim
Journal: Ibn Al-Haitham Journal For Pure And Applied Science مجلة ابن الهيثم للعلوم الصرفة والتطبيقية ISSN: 16094042 Year: 2019 Volume: 32 Issue: 2 Pages: 62-70
Publisher: Baghdad University جامعة بغداد

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Abstract

The objective of this paper is, first, study a new collection of sets such as –field and we discuss the properties of this collection. Second, introduce a new concepts related to the –field such as measure on –field, outer measure on –field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on –field as a generalization of the concept of measure on –field. Furthermore, we establish new concept related to - field noted by weakly null-additive on –field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function on –field and many of its properties and characterizations are given.Keywords: –field, measure on –field, monotone measure, null-additive.

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