Distributions and measures on the boundary of a tree (Q1827072)

The authors study some classes of distributions, relating them to one another and to the space of Borel measures. One main result rests on a property introduced, namely ``absolute summability'' for distributions: a distribution \(\mu\) on \(\Omega\) is called absolutely summable if for any countable collection \((I_n)\) of pairwise disjoint intervals, \(\sum\mu(I_n)\) is absolutely convergent. Then it is proved that the space of measures is identical to the space of distributions which are absolutely summable.