In a previous paper – [17] – we characterized strong measure zero sets of reals in terms of a Ramseyan partition relation on certain subspaces of the Alexandroff duplicate of the unit interval. This framework gave only indirect access to the relevant sets of real numbers. We now work more directly with the sets in question, and since it costs little in additional technicalities, we consider the...

We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result [3] is presented. 2000 Mathematics Subject Classification: 28A05, 28D05.

A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure. For every t > 0 we show that in this category there exists a unique free Borel system (Y, S) which is strictly t-universal in the sense that all invariant me...

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis Paris. line of research was initiated by question Haight and Weizsäker concerning almost everywhere convergence properties series form $\sum_{n=1}^{{\infty}}f(nx)$. A more general, additive version this problem following: Suppose $\Lambda$ discrete infinite set nonnegative real numbers. We say that $ {\Lamb...