Adriaan Cornelis Zaanen: Linear Analysis Measure And Integral, Banach And Hilbert Space, Linear Integral Equations

The present work is devoted to some mathematical theories which all of them may claim to belong to the domain of "linear analysis" It will, however, be clear that it is impossible to comprise everything that might deserve to be so designated into a book of moderate size. The central and larger part of the book (Ch. 6—12) is formed by an introduction to Banach space and Hilbert space, and to some aspects of the theory of bounded and compact linear transformations in these spaces. In order to have at hand non-trivial examples by which to illustrate this theory, the necessity arises to make an appeal to such notions as Lebesgue measure and integral, and Lebesgue function spaces Lp. It is to a concise discussion of these subjects, complete in itself but leaving aside everything which is unessential for the applications in question, that Part I (Ch. 1—5) is devoted. The emphasis is on the algebraic aspects of measure and integral, and topological notions are only introduced when discussing special examples such as Lebesgue or Stieltjes integrals.