# measure zero

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## measure zero

[′mezh·ər ‚zir·ō]
(mathematics)
A set has measure zero if it is measurable and the measure of it is zero.
A subset of Euclidean n-dimensional space which has the property that for any positive number ε there is a covering of the set by n-dimensional rectangles such that the sum of the volumes of the rectangles is less than ε.
References in periodicals archive ?
This definition of measure zero is equivalent to definition arising from Lebesgue measure.
The set A is of measure zero in M if and only if for every coordinate coordinate system (V, h), the set ([pi] o h) (A [intersection] V) is of measure zero in [R.
1] (A) is of measure zero, then A is of measure zero.
So it suffices to show that if B is of measure zero, g (B) is of measure zero.
h(D)] arbitrarily small, it must be the case that h (B [intersection] V) is of measure zero.
2]) will be of measure zero if and only if ([pi] o [h.
3] will be of measure zero in [Real part] if and only if ([?
When we say, as was done in Theorem 4, that a subset A of R is of measure zero in R, we take this to mean that A is of measure zero in the manifold [Real part].
We will show that A is of measure zero and that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = 0 for every ([v.
If the dimension of V is zero, then S = V, and if the dimension of V is positive, then S is of measure zero in V.

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