An outer measure on is Borel regular if, for each set , there exists a Borel set such that . The -dimensional Hausdorff outer measure is regular on .
Regular Borel Measure
See alsoBorel Measure, Hausdorff Measure
This entry contributed by Samuel Nicolay
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ReferencesFalconer, K. J. The Geometry of Fractal Sets. Cambridge, England: Cambridge University Press, 1985.
Referenced on Wolfram|AlphaRegular 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