Abstract
AbstractWe identify simple universal properties that uniquely characterize the Lebesgue spaces. There are two main theorems. The first states that the Banach space , equipped with a small amount of extra structure, is initial as such. The second states that the functor on finite measure spaces, again with some extra structure, is also initial as such. In both cases, the universal characterization of the integrable functions produces a unique characterization of integration. We use the universal properties to derive some of the basic elements of integration theory. We also state universal properties characterizing the sequence spaces and , as well as the functor taking values in Hilbert spaces.
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.
