TY - JOUR
ID -
TI - Some Properties for the Restriction of P^*–field of Sets
AU - Hind F. Abbas
AU - Hassan H. Ebrahim
AU - Ali Al-Fayadh
PY - 2022
VL - 35
IS - 3
SP - 155
EP - 160
JO - Ibn Al-Haitham Journal For Pure and Applied Sciences مجلة ابن الهيثم للعلوم الصرفة والتطبيقية
SN - 16094042 25213407
AB -
The restriction concept is a basic feature in the field of measure theory and has many important properties. This article introduces the notion of restriction of a non-empty class of subset of the power set on a nonempty subset of a universal set. Characterization and examples of the proposed concept are given, and several properties of restriction are investigated. Furthermore, the relation between the P*–field and the restriction of the P*–field is studied, explaining that the restriction of the P*–field is a P*–field too. In addition, it has been shown that the restriction of the P*–field is not necessarily contained in the P*–field, and the converse is true. We provide a necessary condition for the P*–field to obtain that the restriction of the P*–field is included in the P*–field. Finally, this article aims to study the restriction notion and give some propositions, lemmas, and theorems related to the proposed concept.
ER -