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Regular Borel Measure

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer measure H^d is regular on R^n.

See also

Borel Measure, Hausdorff Measure

This entry contributed by Samuel Nicolay

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References

Falconer, K. J. The Geometry of Fractal Sets. Cambridge, England: Cambridge University Press, 1985.

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Regular Borel Measure

Cite this as:

Nicolay, Samuel. "Regular Borel Measure." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RegularBorelMeasure.html

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