The Bochner Integral

By brick functions we will understand, exactly as in Chapter I, characteristic functions of bricks. By a vector valued step function f we mean a function which can be represented in the form $$f = \lambda_1 f_1 + \cdot \cdot \cdot + \lambda_n f_n,$$ where f 1,..., f n are brick functions and λ1,..., λ n are elements of a given normed space. (Note that we do not preserve the convention from Chapter I, concerning the meaning of Latin and Greek letters.