On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field

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Hassan H. Ebrahim Ibrahim S. Ahmed

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.

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How to Cite
EBRAHIM, Hassan H.; AHMED, Ibrahim S.. On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 32, n. 2, p. 62-70, may 2019. ISSN 2521-3407. Available at: <http://jih.uobaghdad.edu.iq/index.php/j/article/view/2140>. Date accessed: 18 june 2019. doi: http://dx.doi.org/10.30526/32.2.2140.
Section
mathematics