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Published online by Cambridge University Press:  13 March 2019

Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus e-mail:
Department of Mathematics, National University of Ireland Maynooth, Maynooth, Kildare, Ireland e-mail:


In this paper, we provide two new extensions to a lemma of Bernik (1983). Applications are also discussed.

Research Article
Copyright © Glasgow Mathematical Journal Trust 2019

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