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We consider a quasi-regular Dirichlet form. We show that a bounded signedmeasure charges no set of zero capacity associated with the form if and only ifthe measure can be decomposed into the sum of an integrable function and abounded linear functional on the domain of the form. The decomposition allowsone to describe explicitly the set of bounded measures charging no sets of zerocapacity for interesting classes of Dirichlet forms. By way of illustration,some examples are given.

On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form