Convergence in measure and in category, similarities and differences
Tóm tắt
Convergence in category of a sequence of real-valued functions has been introduced by E. Wagner as an analogue of convergence in measure. In the paper it is shown that in some circumstances both kinds of convergence behave similarly, but sometimes the behaviour is different.
Tài liệu tham khảo
Bary, N.: Trigonometric series. Moscow (1961) (in Russian)
Bingham N.H., Goldie C.M.: On one-sided Tauberian conditions. Analysis 3, 159–188 (1983)
Bingham N.H., Ostaszewski A.J.: The Steinhaus theorem and regular variation: de Bruijn and after. Indag. Math. 24, 679–692 (2013)
Ciesielski, K., Larson, L., Ostaszewski, K.: \({\mathcal{I}}\)-density continuous functions. Memoirs of the AMS 515, (1994)
Dudley R.M.: Real analysis and probability. Cambridge Studies in Advanced Mathematics, 74. Cambridge University Press, Cambridge (2002)
Halmos, P.R.: Measure Theory. D.Van Nostrand Company (1950) (Graduate Texts in Math. 18, Springer (1979))
Miller, A.W.: Special subsets of the real line In: Kunen, K., Vaughan, J.E. (eds.), Handbook of set-theoretic topology, pp. 201–233, North Holland (1984)
Miller, A.W.: Special sets of reals. In: Set Theory of the Reals, Israel Math. Conference Proceedings 6, pp. 415-432 (1993) American Math. Soc. Editor Haim Judah
Miller H.I., Ostaszewski A.J.: Group actions and shift-compactness. J. Math. Anal. Appl. 392, 23–39 (2012)
Oxtoby J.C.: Measure and Category. Springer, New York (1971)
Solecki S.: Amenability, free subgroups, and Haar null sets in non-locally compact groups. Proc. Lond. Math. Soc. (3) 93(3), 693–722 (2006)
Wagner E.: Sequences of measurable functions. Fund. Math. CXII, 89–102 (1981)
Wilczyński, W., Kharazishvili, A.: On the translations of measurable sets and sets with the Baire property. Bull. of the Acad. of Sciences of Georgia 145,1, pp. 43-46 (1992) (in Russian, English and Georgian summary)