fadaye.mehraboniat

We define an abstract framework for self-similar vector-valued Borel measures on a compact space X based upon a formulation of Iterated Function Systems (IFS) on such measures. This IFS method permits the construction of tangent and normal vector measures to planar fractal curves. Line integrals of smooth vector fields over planar fractal curves may then be defined. These line integrals then lead to a formulation of Greenʹs Theorem and the Divergence Theorem for planar regions bounded by fractal curves. The abstract setting also naturally leads to “probability measure”-valued measures. These measures may be used to color the geometric attractor of an IFS in a self-similar way.