Abstract
For every ordinal ξ<ω1 we define a new type of convergence for sequences of functions (ξ-uniform pointwise) which is intermediate between uniform and pointwise convergence. Using this type of convergence we obtain an Egorov type theorem for sequences of measurable functions.
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References
Alspach, D. and Argyros, S.: Complexity of weakly null sequences, Dissertations Mathematicae CCCXXI (1992), 1–44.
Alspach, D. and Odell: Averaging null sequences, Lectures Notes in Math. 1332, Springer, Berlin 1988.
Bartle, R.: An extension of Egorov's theorem,Amer. Math. Monthly 87 (1980), 628–633.
Egoroff, D.: (D. Egorov), Sur les suites des fonctions mesurables, Comptes Rendus Acad. Sci. Paris, 152 (1911), 244–246.
Kiriakouli, P.: A generalization of classical Ramsey theorem and some applications to Banach spaces theory, submitted.
Mercourakis, S.: On Cesaro summable sequences of continuous functions, Mathematica, 42 (1995), 87–104.
Mercourakis, S.: On some generalizations of the classical Banach-Saks properties, preprint.
Papanastassiou, N. and Kiriakouli, P.: A classification of weakly null sequences, submitted.
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Papanastassiou, N., Kiriakouli, P. Convergence for Sequences of Functions and an Egorov Type Theorem. Positivity 7, 149–159 (2003). https://doi.org/10.1023/A:1026274632150
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DOI: https://doi.org/10.1023/A:1026274632150