Abstract
It was mentioned that to set up a theory of measure capable of measuring the greatest number of subsets in a given space, Lebesgue started with their outer measure \(m^*\), dropped the property of invariance under complements and as counterpart defined inner measures in terms of outer measures of complements. Moreover, in order to satisfy suitable conditions for a measure (such as complete additivity), Lebesgue restricted the domain of the set function \(m^*\) to the class of Lebesgue measurable sets, so the outer measure \(m^*\) will be called the Lebesgue measure m for such sets.
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.
