Abstract
It is shown that any quadratic functional q : R → R whose restriction to a second category Baire subset of R is continuous must be continuous on the whole real line. For this purpose we investigate regularity properties of quadratic functionals with a continuous restriction on an analytic set containing 1 2 (H + H) , where H is a Hamel basis of R . We also prove that for any Baire set T ⊂ R of the second category there exists a Hamel basis H ⊂ R such that 1 2 (H + H) ⊂ T .
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.
