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Here are a few characterizations of derivatives:

  1. On Characterizing Derivatives

    1. D. Preiss and M. Tartaglia On Characterizing Derivatives Proceedings of the American Mathematical Society, Vol. 123, No. 8 (Aug., 1995), pp. 2417-2420.

    2. Chris Freiling, Chris On the problem of characterizing derivatives., Real Anal. Analysis Exchange 23 (1997/98), no. 2, 805–812805-812.

    3. Brian S. Thomson,
      ON RIEMANN SUMS, On Riemann Sums Real Analysis Exchange Vol. 37(1), 2011/2012, pp37 (2011/12), 1-22. 1–22[You can download the PDF file here.]

    The problem was first posed by W. H. Young. We include in our article about the Youngs a full quote stating his problem;

    Bruckner, Andrew M. and Thomson, Brian S. Real variable contributions of G. C. Young and W. H. Young. Expo. Math. 19 (2001), no. 4, 337–358. [You can download the PDF file here.]
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Here are a few characterizations of derivatives:

  1. On Characterizing Derivatives D. Preiss and M. Tartaglia Proceedings of the American Mathematical Society, Vol. 123, No. 8 (Aug., 1995), pp. 2417-2420

  2. Freiling, Chris On the problem of characterizing derivatives.
    Real Anal. Exchange 23 (1997/98), no. 2, 805–812.

  3. Brian S. Thomson,
    ON RIEMANN SUMS, Real Analysis Exchange Vol. 37(1), 2011/2012, pp. 1–22

[You can download the PDF file here: www.classicalrealanalysis.info/documents/Thomson_37.1.pdf.]

The problem was first posed by W. H. Young. We include in our article about the Youngs a full quote stating his problem;

Bruckner, Andrew M. and Thomson, Brian S. Real variable contributions of G. C. Young and W. H. Young. Expo. Math. 19 (2001), no. 4, 337–358.

[You can download the PDf PDF file here:
http://classicalrealanalysis.info/documents/BT-YoungsArticle.pdf.]
show/hide this revision's text 1

Here are a few characterizations of derivatives:

  1. On Characterizing Derivatives D. Preiss and M. Tartaglia Proceedings of the American Mathematical Society, Vol. 123, No. 8 (Aug., 1995), pp. 2417-2420

  2. Freiling, Chris On the problem of characterizing derivatives.
    Real Anal. Exchange 23 (1997/98), no. 2, 805–812.

  3. Brian S. Thomson,
    ON RIEMANN SUMS, Real Analysis Exchange Vol. 37(1), 2011/2012, pp. 1–22

[You can download the PDF file here: www.classicalrealanalysis.info/documents/Thomson_37.1.pdf]

The problem was first posed by W. H. Young. We include in our article about the Youngs a full quote stating his problem; Bruckner, Andrew M. and Thomson, Brian S. Real variable contributions of G. C. Young and W. H. Young. Expo. Math. 19 (2001), no. 4, 337–358.

[You can download the PDf file here:
http://classicalrealanalysis.info/documents/BT-YoungsArticle.pdf]