Real Analysis Exchange

The ℐ-almost constant convergence of sequences of real functions.

Tomasz Natkaniec

Abstract

Let $T$ be an infinite set and $\mathcal{I}$ be a fixed ideal on $T$. We introduce and study the notion of almost constant convergence of sequences $\{ f_t\colon t\in T\}$ of real functions with respect to the ideal $\mathcal{I}$. This notion generalizes discrete convergence, transfinite convergence, and $\omega_2$-convergence. In particular, we consider the question when a given family of functions (e.g., continuous, Baire class 1, Borel measurable, Lebesgue measurable, or functions with the Baire property) is closed with respect to this kind of convergence.

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 481-492.

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.rae/1184963811

Mathematical Reviews number (MathSciNet)
MR2010331

Citation

Natkaniec, Tomasz. The ℐ-almost constant convergence of sequences of real functions. Real Anal. Exchange 28 (2002), no. 2, 481--492. https://projecteuclid.org/euclid.rae/1184963811

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