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The rectifiable sets include the image of any Lipschitz Function 
from planar domains into 
. The
full set is obtained by allowing arbitrary measurable subsets of countable unions of such images of Lipschitz
functions as long as the total Area remains finite. Rectifiable sets have an ``approximate'' tangent plane
at almost every point.
References
Morgan, F. ``What is a Surface?'' Amer. Math. Monthly 103, 369-376, 1996.