We prove a new existence theorem pertaining to the Plateau problem in -dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.
We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators.
For homographic extensions of the one-sided Bernoulli shift we construct σ-finite invariant and ergodic product measures. We apply the above to the description of invariant product probability measures for smooth extensions of one-sided Bernoulli shifts.
A necessary condition is given for the existence of the tensor product of certain measures valued in locally convex spaces.
In this note we define three variations for a vector valued function defined on an inf-semilattice, all of them generalizations of those considered for vector valued set-functions. We are interested in additive and finiteness properties of such variations.