If the boundary is rectifiable, then one can calculate the measure as an integral, in a manner analogous to the calculation of arc length and surface area in basic multivariable calculus.
22.
Let \ gamma be a loop in \ textstyle \ overline { U } which is uniform limit of a sequence \ gamma _ k of rectifiable loops in " U " with bounded lengths.
23.
This is a very small issue in the overall biographical summary, but still constitutes an easily rectifiable omission, IMO . As such I continue to "'Support "'my original close.
24.
Then M is m-rectifiable if and only if there exists a positive locally \ mathcal { H } ^ m-integrable function \ theta : M \ to ( 0, \ infty ) such that the Radon measure
25.
Menger curvature, as in the previous example, can be used to give numerical estimates that determine whether a set contains a rectifiable subset, and the proofs of these results frequently depend on " ? "-numbers.
26.
By using the Cauchy integral theorem, one can show that the integral over " C " ( or the closed rectifiable curve ) is equal to the same integral taken over an arbitrarily small circle around " a ".
27.
If a polyomino is rectifiable, or able to tile a rectangle, then it will also be a rep-tile, because the rectangle can be used to tile a square ( which is itself a special case of the rectangle ).
28.
If " S " is a rectifiable hypersurface completely enclosing " K ", then the harmonic capacity can be equivalently rewritten as the integral over " S " of the outward normal derivative of " u ":
29.
Here " ? " is a rectifiable path in a simply connected open subset " U " of the complex plane "'C "'whose start point is equal to its end point, and is a holomorphic function.
30.
:" The Bible teaches that God s intention for humankind is that society should be ordered on the basis of lifelong, legally sanctioned heterosexual unions . . . . A disposition towards homosexuality is not in itself blameworthy nor is the disposition seen as rectifiable at will . . . . Homosexual practice however, is, in the light of Scripture, clearly unacceptable.
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