Abstract
Abstract Let 𝓙 be an ideal on ℕ which is analytic or coanalytic. Assume that (fn ) is a sequence of functions with the Baire property from a Polish space X into a Polish space Z, which is divergent on a comeager set. We investigate the Baire category of 𝓙-convergent subsequences and rearrangements of (fn ). Our result generalizes a theorem of Kallman. A similar theorem for subsequences is obtained if (X,μ) is a σ-finite complete measure space and a sequence (fn ) of measurable functions from X to Z is 𝓙-divergent μ-almost everywhere. Then the set of subsequences of (fn ), 𝓙-divergent μ-almost everywhere, is of full product measure on {0,1}ℕ. Here we assume additionally that 𝓙 has property (G).
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.
