“…In this section, we summarize several basic properties of regular Dirichlet extensions or subspaces, which are contained in [12][13][14][15][16]18]. We always fix two regular Dirichlet forms (E 1 , F 1 ) and (E 2 , F 2 ) on L 2 (E, m) and assume that (E 1 , F 1 ) is a regular Dirichlet subspace of (E 2 , F 2 ), equivalently (E 2 , F 2 ) is a regular Dirichlet extension of (E 1 , F 1 ).…”