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In this paper, we shall explore the Mosco convergence on regular subspaces ofone-dimensional irreducible and strongly local Dirichlet forms. We find that ifthe characteristic sets of regular subspaces are convergent, then theirassociated regular subspaces are convergent in sense of Mosco. Finally, weshall show some examples to illustrate that the Mosco convergence does notpreserve any global properties of Dirichlet forms.

Regular Dirichlet subspaces and Mosco convergence