Abstract
The concept of a measurable function was introduced by Lebesgue when constructing integration theory. Later, Luzin established the so-called C-property of measurable functions which, roughly speaking, can be formulated as follows: Every measurable function is “almost continuous”. In this chapter, we study the properties of measurable functions and investigate different types of convergence of sequences of measurable functions and relations between them. In the last section, the C-property is proved.KeywordsMeasurable FunctionMeasurable SpaceSimple FunctionBorel SubsetFinite MeasureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
