ABSTRACT
This chapter considers the integrability of a-stable processes. For a process to be integrable, it must be measurable. The chapter discusses the necessary and sufficient conditions for measurability in terms of the integral representation of the process. It also considers absolute continuity. Absolute continuity implies the existence of a derivative. The chapter describes about Measurability, integrability and absolute continuity with the use of theorems, corollaries, and some examples. It deals with integrability of the sample paths of stable processes, conditions for integrability, changing the order of integration, tail behavior of the Lp-norm distribution, and absolute continuity of stable processes with the use of some theorems and examples.
