It is of great importance to compare the correlation of different XML (extensible markup language) streams in the limited space in the Database Theory. In the study of these problems, several measures are proposed, e.g. the tree-edit distance, to show the difference of XML trees. This paper proposes a natural measure l₀ employing Hamming norms, i.e. the number of distinct sub-trees between two XML trees, to estimate the correlation. Furthermore, a probabilistic estimating algorithm involving space-bounded pseudorandom generators, stable distributions and hash functions has been presented in the data stream model. Theoretical time/space complexity analysis, correctness proof and experimental simulation show that this algorithm can give a desired approximation.