Publisher Summary This chapter describes the Lebesgue Spaces Lp(Ω). The chapter assumes Ω as a domain in Rn and p as a positive real number. The chapter denotes by Lp (Ω) the class of all measurable functions u that is defined on Ω. The chapter also identifies in Lp (Ω) functions that are equal almost everywhere in Ω; the elements of Lp (Ω) are thus equivalence classes of measurable functions satisfying two functions being equivalent if they are equal a.e. in Ω.