The paper considers the capacity of a polycondenser and the module of a family of measures associated with the class of curves connecting the polycondenser’s plates. It is proved that these quantities are equal. Also a relation between the polycondenser’s capacity and the module of a family of vector measures associated with the class of functions admissible for the polycondenser’s capacity is established. The results obtained generalize the earlier results by M. Ohtsuka and H. Aikawa.
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Dedicated to the 80th anniversary of Igor' Petrovich Mityuk's birthday
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 56–68.
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Dymchenko, Y.V., Shlyk, V.A. Polycondenser’s capacity and the module of a family of vector measures. J Math Sci 166, 155–161 (2010). https://doi.org/10.1007/s10958-010-9855-7
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DOI: https://doi.org/10.1007/s10958-010-9855-7