  We define a $\sigma$-centered notion of forcing that forces the existence of
a Boolean algebra with the Grothendieck property and without the Nikodym
property. In particular the existence of such an algebra is consistent with the
negation of the continuum hypothesis. The algebra we construct consists of
Borel subsets of the Cantor set and has cardinality $\omega_1$. We also show
how to apply our method to streamline Talagrand's construction of such an
algebra under the continuum hypothesis.
