Three kinds of convergence and the associated -Baire classes

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• 作者：Rafał ; Filipó ; w ^{rfilipow@mat.ug.edu.pl} ; Piotr Szuca ; ^{pszuca@radix.com.pl}
• 关键词：Ideal convergence ; Convergence of sequences of functions ; Discrete convergence ; Equal convergence ; Baire classification of functions ; Scatteredly continuous functions ; Baire one star functions ; Borel ideal ; Analytic ideal ; Laflamme game ; Filter convergenc
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 July, 2012
• 卷：391
• 期：1
• 页码：1-9
• 文件大小：192 K

摘要

We consider ideal versions of pointwise, discrete and equal convergence of sequences of functions. Defining, in a natural way, ideal pointwise (discrete, equal) Baire classes of functions, we show that these classes are equal to their classical counterparts for ideals for which there is a winning strategy in a game introduced by Laflamme (1996) . In the proofs we make extensive use of a characterization (in terms of filters which are 蠅-diagonalizable by -universal sets) of a winning strategy. This article extends results of Laczkovich and Rec艂aw (2009) , and Debs and Saint Raymond (2009) .