The Law of Large Numbers of the Size of Complete Interval Trees

In this paper, we mainly discuss the law of large numbers of Sx, the number of vertexes on an complete interval tree. The method we use is much different from that was used in the case of one-side interval trees. First, we discuss the probability space, on which the interval trees are defined; and make clean its construction, which is the foundation for researching the strong law of large numbers. Second, considering that the moment generation functions of r.v. Sx are difficult to obtain, we use a new method to calculate its expectations and variations. Finally, we prove the weak and strong law of large numbers of r.v Sx.