  By using Bernstein-type inequality we define analogs of spaces of entire
functions of exponential type in $L_{p}(X), 1\leq p\leq \infty$, where $X$ is a
symmetric space of non-compact. We give estimates of $L_{p}$-norms, $1\leq
p\leq \infty$, of such functions (the Nikolskii-type inequalities) and also
prove the $L_{p}$- Plancherel-Polya inequalities which imply that our functions
of exponential type are uniquely determined by their inner products with
certain countable sets of measures with compact supports and can be
reconstructed from such sets of "measurements" in a stable way.
