Algebre di Von Neumann e Teoria della Misura Non Commutativa

This thesis presents an introduction to the vast subject of Von Neumann algebras, with a peculiar attention to the abelian case and its connection to the measure theory. More precisely, the aim of this work is to show the equivalence between the study of abelian Von Neumann algebras on one side and that of (locally) compact measure spaces on the other, a result which is achieved by identifying a general abelian Von Neumann algebra with a space of bounded functions on a suitable compact space.