ABSTRACT
This chapter devotes to considering the predual. The dual of Morrey spaces contains an element which cannot be expressed in terms of locally integrable functions. The chapter shows that Morrey spaces are realized as the dual of Banach function spaces. One of the reasons why such a situation occurs is that Morrey spaces are wider than Lebesgue spaces. The Fatou property of the function spaces is one of the important properties. As it turns out, among others it is difficult to check the Fatou property of predual spaces. One of the fundamental techniques in the theory of function spaces is to decompose functions into some elementary pieces. There are couple of integration theories, Lebesgue integral, Riemannian integral, Henstock integral and so on. Choquet integral is one of the integration theories. Kothe and Toeplitz began the study of certain pairs of subspaces of the space of all real sequences.
