Generalizations of σ–field and new collections of sets noted by δ–field

In this paper, we introduce some new collections of sets such as α– σ–field and β– σ–field as two generalizations of the notion of σ–field and we discuss the properties of these collections. Furthermore, we study the relationships between α– σ–field and σ–field. As a first result, we prove that every σ–field is α– σ–field and β– σ–field. Finally, we establish new collection of sets such as δ–field and obtain some results deals with this concept and we conclude that each of α– σ–field and β– σ–field are generalizations of δ–field.