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.