Before revision:  Our main result is that if x_1,\ldots, x_n are i.i.d. ~ samples from a d-Ahlfors regular measure on a metric space, and E  _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
After revision:  Our main result is that if x_1,\ldots, x_n are i.i.d. samples from a d-Ahlfors regular measure on a metric space, and E _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n: