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.
Rectifiable Set
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References
Morgan, F. "What is a Surface?" Amer. Math. Monthly 103, 369-376, 1996.Referenced on Wolfram|Alpha
Rectifiable SetCite this as:
Weisstein, Eric W. "Rectifiable Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RectifiableSet.html