Real Analysis Exchange

Convergence and Kolmogorov dimension

M. Scott Osborne

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Abstract

It is shown that under simple restrictions a series converges provided it’s set of terms has Kolmogorov dimension strictly smaller than \(\frac{1}{2}\).

Article information

Source
Real Anal. Exchange, Volume 21, Number 1 (1995), 264-269.

Dates
First available in Project Euclid: 3 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1341343241

Mathematical Reviews number (MathSciNet)
MR1377535

Zentralblatt MATH identifier
0847.40001

Subjects
Primary: 40A05: Convergence and divergence of series and sequences 54F45: Dimension theory [See also 55M10]

Keywords
Kolmogorov dimension

Citation

Osborne, M. Scott. Convergence and Kolmogorov dimension. Real Anal. Exchange 21 (1995), no. 1, 264--269. https://projecteuclid.org/euclid.rae/1341343241


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References

  • B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982.
  • C. Essex and M. Nerenberg, Fractal dimension: Limit capacity or Hausdorff dimension?, Am. J. Phys., 58 (10), (1990), 986–8.