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Pointwise Dimension

A pointwise dimension is defined by

D_P(x)=lim_(epsilon->0)(lnmu(B_epsilon(x)))/(lnepsilon),

where B_epsilon(x) is an n-dimensional ball of radius epsilon centered at x and mu is the probability measure.

See also

Ball, Probability Measure

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References

Nayfeh, A. H. and Balachandran, B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. New York: Wiley, pp. 541-545, 1995.

Referenced on Wolfram|Alpha

Pointwise Dimension

Cite this as:

Weisstein, Eric W. "Pointwise Dimension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PointwiseDimension.html

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