ON SUMES OF ALMOST PERIODIC (A.P.) MULTI-VALUED FUNCTIONS
Keywords:
Almost periodic multivalued functions, spaces R^n, equivalence, arbitrary infinite sequence, real numbers, Sum of multivalued numbersAbstract
This paper examines the basic properties of the sum of almost periodic multivalued functions whose values are compact sets of the space R^n. It is much more difficult to prove that the sum of two almost-periodic (a.p.) multi-valued functions is a multi- valued a.p. function. The first proof of this theorem for a single-valued function was given by G.Bohr. Subsequently, Bochner gave others a definition for unambiguous a.p. functions on which the almost-periodicity of the sum follows directly. Subsequently, it turned out that Bochner’s definition is very useful in many other questions of the theory of a.p. functions. Let us now give a definition for multi- valued a.p. functions, according to Bochner, and prove the equivalence of this definition with Bohr’s definition.
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