  We prove a Hilbert-Samuel type result of arithmetic big line bundles in
Arakelov geometry, which is an analogue of a classical theorem of Siu. An
application of this result gives equidistribution of small points over
algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also
generalize Chambert-Loir's non-archimedean equidistribution.
