Real Analysis Exchange

On Lacuna's 7-tuples for Ideal Convergence

Dariusz Borzestowski and Ireneusz Recław

Full-text: Open access


We prove the ideal versions of Lunina's Theorem on convergence and divergence sets of real continuous functions defined on a metric space for $F_\sigma$-ideals and ideals with Baire property.

Article information

Real Anal. Exchange, Volume 35, Number 2 (2009), 479-486.

First available in Project Euclid: 22 September 2010

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
Secondary: 03E15: Descriptive set theory [See also 28A05, 54H05]

ideal convergence continuous functions convergence sets Lunina's theorem


Borzestowski, Dariusz; Recław, Ireneusz. On Lacuna's 7-tuples for Ideal Convergence. Real Anal. Exchange 35 (2009), no. 2, 479--486.

Export citation


  • A. R. Bernstein, A new kind of compactness for topological spaces, Fund. Math., 66 (1969/1970), 185–193.
  • K. Dems, On J-Cauchy sequences, Real Anal. Exchange, 30 (2004/05), 123–128.
  • I. Farah, Analytic quotients: theory of liftings for quotients over analytic ideals on the integers, Mem. Amer. Math. Soc., 148(702) (2000).
  • H. Fast, Sur la convergence statistique. Colloq. Math., 2 (1951), 241–244.
  • M. Katětov, Products of filters. Comment. Math. Univ. Carolin., 9 (1968), 173–189.
  • M. A. Lunina, Sets of convergence and divergence of a sequences of real-valued continuous functions on a metric space, Math. Notes, 17 (1975), 120–126.
  • K. Mazur, $ F_{\sigma} $-ideals and $ \omega_{1} \omega_{1}^{\star}$-gaps in the Boolean algebras $ \pomega/I $, Fund. Math., 138 (1991), 103–111.
  • M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math., 67(1) (1980), 13–43.