Abstract
In this chapter, the concept of a measure is defined, and some of its basic properties are established. We then proceed with the introduction of an outer measure, study its relationship to the underlying measure, and determine the class of sets measurable with respect to the outer measure. These results are used as a basis toward obtaining an extension of a given measure from a field to the σ-field generated by this field. Next, by means of a measure, a class of point real-valued functions is defined, and their basic properties are studied. Finally, it is shown that any nondecreasing right-continuous function induces a unique measure in the Borel real line.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
