ABSTRACT
The notion of positivity in concrete function spaces is very important, in theory as well as in application. Many important results have been obtained by a systematic abstract treatment of the positivity in linear spaces. These results are called the theory of vector lattices as point functions, and the representation of a vector lattice as a set of functions is discussed in book [1]. In this paper, let the vector lattice X have the principal projection property and e Є AT+. If x is a given element in the band generated by e, we give the spectral representation of x. The Radon-Nikodyn theorem in measure theory is a particular case of the spectral representation in vector lattices.
