A rectifiable curve is a curve with finite length. An integral current is an integer rectifiable current whose boundary has finite mass. Loosely speaking, rectifiable sets are precisely those for which approximate tangent spaces exist almost everywhere. One consequence is that sets with positive and finite density are rectifiable sets. Suppose formula 1 is a rectifiable plane curve. That is, these curves are a subset of the rectifiable curves. The notion of approximate tangent spaces is very closely related to that of rectifiable sets. Let formula 35 be a rectifiable curve on a plane. The Cantor function is non-decreasing, and so in particular its graph defines a rectifiable curve. The relationship holds for figures that are not rectifiable as well. Varifolds generalize the idea of a rectifiable current, and are studied in geometric measure theory. Now suppose that formula 185 is rectifiable, and set formula 186. Rectifiable sets are the underlying object of study in geometric measure theory. If formula 29 is a Lipschitz-continuous function, then it is automatically rectifiable. In other words, the curve is always rectifiable.