2,674 research outputs found
Congruent families and invariant tensors
Classical results of Chentsov and Campbell state that -- up to constant
multiples -- the only -tensor field of a statistical model which is
invariant under congruent Markov morphisms is the Fisher metric and the only
invariant -tensor field is the Amari-Chentsov tensor. We generalize this
result for arbitrary degree , showing that any family of -tensors which
is invariant under congruent Markov morphisms is algebraically generated by the
canonical tensor fields defined in an earlier paper
Parametrizing the abstract Ellentuck theorem
We give a parametrization with perfect sets of the abstract Ellentuck
theorem. The main tool for achieving this goal is a sort of parametrization of
an abstract version of the Nash-Williams theorem. As corollaries, we obtain
some known classical results like the parametrized version of the Galvin-Prikry
theorem due to Miller and Todorcevic, and the parametrized version of
Ellentuck's theorem due to Pawlikowski. Also, we obtain parametized vesions of
nonclassical results such as Milliken's theorem.Comment: 16 pages. Submitted to Elsevier's Discrete Mathematic
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