Abstract: Using the method of Markov operator to measure function, we investigated the relationship between probability measure of the typical fractal sets and Dirac measure of Cantor division set, Sierpinski right triangle and Koch curve based on hyperbolic iterated function system under the condition of equal probability,  and obtained the relationship between probability measure and Dirac measure on the more general fractal sets under equal probability and unequal probability, respectively.

Key words:  hyperbolic iterated function system with probability (hyperbolic IFSP), attractor, Dirac measure, probability measure