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On F\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F$$\\end{document}-spaces of almost-Lebesgue functions
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On F\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F$$\\end{document}-spaces of almost-Lebesgue functions
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Journal Article
On F\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F$$\\end{document}-spaces of almost-Lebesgue functions
2025
Overview
We consider the space of functions almost in Lp and endow it with the topology of asymptotic Lp -convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of measurable functions equipped with the topology of (local) convergence in measure. We investigate analogs of classical results such as dominated convergence and Vitali convergence theorems. For Rd as the underlying measure space, we establish results on approximation by smooth functions and separability. Further aspects, including local boundedness, local convexity, and duality are examined in the Rd setting, revealing fundamental differences from standard Lp spaces.
Publisher
Springer Nature B.V
Subject
