On weak integrability and boundedness in Banach spaces

Abstract. Thin and thick sets in normed spaces were defined and studied by M. I. Kadets and V. P. Fonf in 1983. In this paper, we give a new charac-terization of thick sets in terms of weak integrability of Banach space valued measurable functions. We also characterize thick sets in terms of boundedness of vector measures, and explain how this concept is related to the theory of barrelled spaces. 1