  The von Weizs\"{a}cker theorem states that every sequence of nonnegative
random variables has a subsequence which is Ces\`{a}ro convergent to a
nonnegative random variable which might be infinite. The goal of this note is
to provide a description of the set where the limit is finite. For this
purpose, we use a decomposition result due to Brannath and Schachermayer.
