# The Classes A, B, ℭ

Chapter

## Abstract

The main objective of the present chapter is to prove equality (9.1.2), and to give some characterizations of the classes A, ℭ introduced in the preceding chapter. Thus we do not assume equality (9.1.2) as valid, it will be proved in the sequel^{1}. To this aim we will need a rational version of the Hahn-Banach theorem, which we will presently prove. We start with a definition.

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© Birkhäuser Verlag AG 2009