  The study deals with the theory of interior capacities of condensers in a
locally compact space, a condenser being treated here as a countable, locally
finite collection of arbitrary sets with the sign +1 or -1 prescribed such that
the closures of opposite-signed sets are mutually disjoint. We are motivated by
the known fact that, in the noncompact case, the main minimum-problem of the
theory is in general unsolvable, and this occurs even under very natural
assumptions (e.g., for the Newtonian, Green, or Riesz kernels in an Euclidean
space and closed condensers of finitely many plates). Therefore it was
particularly interesting to find statements of variational problems dual to the
main minimum-problem (and hence providing some new equivalent definitions of
the capacity), but now always solvable (e.g., even for nonclosed, unbounded
condensers of infinitely many plates). For all positive definite kernels
satisfying B. Fuglede's condition of consistency between the strong and
weak-star topologies, problems with the desired properties are posed and
solved. Their solutions provide a natural generalization of the well-known
notion of interior capacitary distributions associated with a set. We give a
description of those solutions, establish statements on their uniqueness and
continuity, and point out their characteristic properties.
