  We study energy measures on SG based on harmonic functions. We characterize
the positive energy measures through studying the bounds of Radon-Nikodym
derivatives with respect to the Kusuoka measure. We prove a limited continuity
of the derivative on the graph $V_*$ and express the average value of the
derivative on a whole cell as a weighted average of the values on the boundary
vertices. We also prove some characterizations and properties of the weights.
