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 alpha-sigma-field and beta-sigma-field as two generalizations of the notion of sigma-field and we discuss the properties of these collections. Furthermore, we study the relationships between alpha-sigma-field and sigma-field. As a first result, we prove that every sigma-field is alpha-sigma-field and beta-sigma-field. Finally, we establish new collection of sets such as delta-field and obtain some results deals with this concept and we conclude that each of alpha-sigma-field and beta-sigma-field are generalizations of delta-field.