On a new kind of collection of subsets noted by δ-field and some concepts defined on δ-field

Abstract EN

The objective of this paper is, first, study a new collection of sets such as 5-field and we discuss the properties of this collection.

Second, introduce a new concepts related to the 5-field such as measure on 5-field, outer measure on 5-field and we obtain some important results deals with these concepts.

Third, introduce the concept of null-additive on 5-field as a generalization of the concept of measure on 5-field.

Furthermore, we establish new concept related to 5- field noted by weakly] null-additive on 5-field as a generalizations of the concepts of measure on and null-additive.

Finally, we introduce the restriction of a set function V on 5-field and many of its properties and characterizations are given.