Radon-Nikodým Derivatives of Hilbert Space Valued Measures
The weak Radon-Nikodým derivative of a Hilbert space valued measure is introduced. We obtain a necessary and sufficient condition for the existence of such a measure and study some of its properties. Integration of a scalar valued function with respect to a Hilbert space valued measure having a weak Radon-Nikodým derivative is seen to be related to the usual Dunford-Schwartz integral. Finally, we examine the case where the measure has values in the class of Hilbert-Schmidt operators.
AMS Subject Classification28B05 60G12
KeywordsHilbert space valued measures Weak Radon-Nikodým derivatives v-boundedness
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