Real Analysis Exchange

Quasi-uniform convergence of sequences of 1-improvable discontinuous functions

Jadwiga Wolnicka

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Abstract

In the paper it is shown that the strongly quasi-uniform limit of a sequence of 1-improvable discontinuous functions on a complete space \(X\) is a 1-improvable discontinuous function or a continuous function. Automatically the same result will be valid for uniform convergence.

Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 750-754.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694105

Mathematical Reviews number (MathSciNet)
MR1407289

Zentralblatt MATH identifier
0879.54017

Subjects
Primary: 54C30: Real-valued functions [See also 26-XX]
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Keywords
1-improvable discontinuous functions quasi-uniform convergence

Citation

Wolnicka, Jadwiga. Quasi-uniform convergence of sequences of 1-improvable discontinuous functions. Real Anal. Exchange 21 (1995), no. 2, 750--754. https://projecteuclid.org/euclid.rae/1339694105


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