Real Analysis Exchange

On A.C. Limits and Monotone Limits of Sequences of Jump Functions

Zbigniew Grande

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Abstract

The a.c. limits (introduced by Császár and Laczkovich) and the monotone limits of sequences of functions having everywhere finite unilateral limits are investigated.

Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 817-828.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995417

Mathematical Reviews number (MathSciNet)
MR1778535

Zentralblatt MATH identifier
1013.26004

Subjects
Primary: 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} 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A99: None of the above, but in this section

Keywords
upper semicontinuity decreasing sequences of functions $B_1^*$ class a.c. convergence jump function

Citation

Grande, Zbigniew. On A.C. Limits and Monotone Limits of Sequences of Jump Functions. Real Anal. Exchange 25 (1999), no. 2, 817--828. https://projecteuclid.org/euclid.rae/1230995417


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References

  • A. M. Bruckner, J. B. Bruckner, and B. S. Thomson, Real Analysis, Prentice–Hall International, INC, Upper Saddle River, New Jersey, 1996.
  • A. Császár and M. Laczkovich, Discrete and equal convergence, Studia Sci. Math. Hungar. 10(1975), 463–472.
  • R. J. O'Malley, Approximately differentiable functions. The r topology, Pacific J. Math. 72(1977), 207–222.
  • C. S. Reed, Pointwise limits of sequences of functions, Fund. Math. 67(1970), 183–193.
  • B. S. Thomson, Real Functions, Lectures Notes in Math. 1170(1985), Springer–Verlag.