Symbolic Spaces And The Existence Of Invariant Measures

This paper deals with,the theory of symbolic space and iterated function system in fractal geometry.By constructing invariant measure in symbolic space,and by using the mapping of symbol space to Rn,the induce measure in Rn is obtained,and it is invariant measure in iterated function system.so a new proof of the existence of invariant measure in Rn space is given.It need to be explained,in the literature[3]a proof is given under the condition that the iterated function system satisfies the strong separation.