On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form
Volume 65 / 2017
Bulletin Polish Acad. Sci. Math. 65 (2017), 45-56
MSC: Primary 31C25; Secondary 46E99, 60J45.
DOI: 10.4064/ba8108-7-2017
Published online: 14 July 2017
Abstract
We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decomposed into the sum of an integrable function and a bounded linear functional on the domain of the form. The decomposition allows one to describe explicitly the set of bounded measures charging no sets of zero capacity for interesting classes of Dirichlet forms. By way of illustration, some examples are given.
