  The regular subspaces of a Dirichlet form are the regular Dirichlet forms
that inherit the original form but possess smaller domains. The two problems we
are concerned are: (1) the existence of regular subspaces of a fixed Dirichlet
form, (2) the characterization of the regular subspaces if exists. In this
paper, we will first research the structure of regular subspaces for a fixed
Dirichlet form. The main results indicate that the jumping and killing measures
of each regular subspace are just equal to that of the original Dirichlet form.
By using the independent coupling of Dirichlet forms and some celebrated
probabilistic transformations, we will study the existence and characterization
of the regular subspaces of local Dirichlet forms.
