The Singular Measure of a Dirichlet Space

Masayuki Itô

doi:10.1017/s0027763000026775

The Singular Measure of a Dirichlet Space

Masayuki Itô

説明

<jats:p>We [4], [5] examined some properties of balayaged measures in the theory of a Dirichlet space. In those papers, we showed that the singular measure of a Dirichlet space plays some important roles. In this paper, we shall precisely examine some properties of the singular measure of a Dirichlet space. Let <jats:italic>X</jats:italic> be a locally compact Hausdorff space in which there exists a positive Radon measure ξ which is everywhere dense in <jats:italic>X</jats:italic>.</jats:p>