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Results of Tadeusz Świątkowski on algebraic sums of sets and their applications in the theory of subadditive functions

Matkowski J.

Journal of Applied Analysis

2012

Vol. 18, nr 1

97-116

A refinement of Steinhaus' theorem on the algebraic sum of subsets of R due to Raikov (1939) was not known to the mathematical community and still is not popular. In 1994, Tadeusz Świątkowski, being not aware of the existence of Raikov's theorem, proved another result of this type. Unfortunately, a few days later he passed away. In this paper we present the theorems of Świątkowski and Raikov and we apply them in the theory of subadditive type inequalities. An improvement of a converse of Minkowski's inequality theorem is presented.