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.
Morgan, F. ``What is a Surface?'' Amer. Math. Monthly 103, 369-376, 1996.