A study on rare $m _x$ sets and rarely $m _x$ continuous functions

A study on rare $m _x$ sets and rarely $m _x$ continuous functions

The aim of this paper is to introduce the concept of rare $m _x$ sets, dense$m _x$ sets and rarely $m _x$ continuous functions. Some properties of these sets are studied and it is shown that only the null set is both a rare$m _x$ set and an open $m _x$ set.

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