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Measure Zero


Measure zero means that a measurable set A has mu(A)=0 for a specified measure mu (Hunter 2011, p. 6).

For Lebesgue measure on R, a set of points has measure zero iff it can be enclosed in a countable family of intervals whose total length is arbitrarily small (Hunter 2011, p. 18).


See also

Almost Everywhere, Lebesgue Measure, Measurable Set, Measure

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References

Hunter, J. K. Measure Theory. Lecture notes, pp. 6 and 18, 2011. https://www.math.ucdavis.edu/~hunter/m206/measure_notes.pdf.Jeffreys, H. and Jeffreys, B. S. "'Measure Zero': 'Almost Everywhere.' " §1.1013 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 29-30, 1988.

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Measure Zero

Cite this as:

Weisstein, Eric W. "Measure Zero." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MeasureZero.html

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