Soft Set Theory & Soft Sigma Algebras

The work presented hereby is completed with help of Dr Muhammad Riaz, Department of Mathematics, University of The Punjab, Lahore, Pakistan and inspiration given by Dr Deeba Afzal, Department of Mathematics & Statistics, The University of Lahore, Pakistan. This notion of Soft Set Theory was introduced by Russian Researcher Molodtsov in 1999. There are many applications of soft set theory in a variety of fields including social sciences, physics, engineering, economics, computer science and medical sciences. Soft set theory is a generalization of crisp set theory. In the present work, we study soft topology on a soft set and extend various properties of crisp topology towards the soft topology. We study soft basis for the soft topology. We also study soft ring of sets, soft sigma ring, soft algebra, and soft sigma algebra. We study various set functions. Furthermore, we introduced the notion of measurable soft mappings. Moreover, we present some fundamental notions related to soft probability measure.