Ideal convergent subsequences and rearrangements for divergent sequences of functions
-
Marek Balcerzak
,
Michał Popławski
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).
Acknowledgement
We would like to thank the Referee who has indicated us some important improvements and corrections.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Paolo de Lucia
- Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
- A note on field-valued measures
- Topologies and uniformities on d0-algebras
- On some properties of 𝓙-approximately continuous functions
- Porous subsets in the space of functions having the Baire property
- Rademacher’s theorem in Banach spaces without RNP
- Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
- Measure games on pseudo-D-lattices
- On some properties of k-subadditive lattice group-valued capacities
- Lp Spaces in vector lattices and applications
- The Choquet integral with respect to fuzzy measures and applications
- A note on the range of vector measures
- Ideal convergent subsequences and rearrangements for divergent sequences of functions
- Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
- A generalization of the exponential sampling series and its approximation properties
- Monotonicity and total boundedness in spaces of “measurable” functions
- Vector lattices in synaptic algebras
- Density, ψ-density and continuity
- Feather topologies
- On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
- Rate of convergence of empirical measures for exchangeable sequences
- On non-additive probability measures
- Equi-topological entropy curves for skew tent maps in the square
- On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
