Two criteria of Wiener type for minimally thin sets and rarefied sets in a cylinder (Q2469777)

As a first result the author proves that a minimally thin at \(\infty\) set in a cylinder is defined by a criterion of Wiener type. Next a rarefied set in a cylinder is defined and it is shown that it is also characterized by a criterion of Wiener type. The regularity of boundary behavior of positive superharmonic function on a cylinder outside a rarefied set is proved. Some connection between a minimally thin set and rarefied set in a cylinder is also given.