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Keywords:
almost periodic function in view of the Lebesgue measure; barrelled space; Bohr almost periodic function; Denjoy-Bochner almost periodic function; Denjoy-Perron integral; Henstock-Kurzweil integral; linear differential equation
almost periodic function in view of the Lebesgue measure; barrelled space; Bohr almost periodic function; Denjoy-Bochner almost periodic function; Denjoy-Perron integral; Henstock-Kurzweil integral; linear differential equation
Summary:
We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.
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