ABSTRACT
The order structure proves to be fundamental even in relation to the more subtle points of integration theory. This fact alone makes some observations about ordered sets indispensable. The existence of suprema and infima in an ordered set is by no means always assured. Their existence distinguishes a large class of ordered sets, namely lattices. This chapter discusses laws that illustrate an important property of lattice operations, namely duality. It describes real-valued functions and extended real-valued functions using lattice operations. Vector lattices can be dealt with as abstract algebraic structures. A vector lattice is a combination of vector space and lattice structures. The chapter also provides a discussion on Daniell spaces.
