  Let $K$ be the scalar field of real numbers or complex numbers and
$L^{0}(\mathcal{F},K)$ the algebra of equivalence classes of $K-$valued random
variables defined on a probability space $(\Omega,\mathcal{F},P)$. In this
paper, we first characterize the algebraic structure of finitely generated
$L^{0}(\mathcal{F},K)$-modules and then combining the recently developed
separation theorem in random locally convex modules we prove the Helly theorem
in random normed modules with the countable concatenation property under the
framework of random conjugate spaces at the same time a simple counterexample
shows that it is necessary to require the countable concatenation property. By
the way,we also give an application to the existence problem of the random
solution of a system of random linear functional equations.
