This chapter is devoted to the study of three fundamental notions: measurable space, measurable function and measure. The concepts of a measurable space and of a measurable function depend in no way upon any measure. However, in practice measurable spaces and measurable functions are almost always used in the presence of measure. This justifies the adoption of the term “measurable” for theirs names.
7 Measurable Spaces
This section is devoted to a detailed study of algebras and -algebras of sets, which are families of sets indispensable for introducing the notions of measurability and measure. As we stated in the beginning ...