In the study of some dynamical systems limsup set a sequence measurable sets is often interest. The shrinking targets and recurrence are two most commonly studied problems that concern sets. However, zero-one laws for usually treated separately proved differently. this paper, we introduce generalized definition can specialize into recurrence; our approach gives unified proof problems.

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

1. A set of S real numbers which has inner measure m*(S) different from its outer measure m*iS) is non-measurable. An extreme form, which we shall call saturated non-measurability, occurs when ra*(S)=0 but m*iSM)=miM) for every measurable set M, miM) denoting the measure of M. This is equivalent to: both S and its complement have zero inner measure. More generally, if a fixed set B of positive ...