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 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.

## Referenced on Wolfram|Alpha

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