The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft rgb-closed set) Moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g$alpha$-closed, soft g$alpha$b-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and w...

We investigate notions of randomness in the space C[2N] of nonempty closed subsets of {0, 1}N. A probability measure is given and a version of the Martin-Löf test for randomness is defined. Π2 random closed sets exist but there are no random Π1 closed sets. It is shown that any random closed set is perfect, has measure 0, and has box dimension log2 4 3 . A random closed set has no n-c.e. elemen...

Algorithmic randomness was originally defined for Cantor space with the fair-coin measure. Recent work has examined algorithmic randomness in new contexts, in particular closed subsets of 2ω ([2] and [8]). In this paper we use the probability theory of closed set-valued random variables (RACS) to extend the definition of Martin-Löf randomness to spaces of closed subsets of locally compact, Haus...