  We construct random locally compact real trees called Levy trees that are the
genealogical trees associated with continuous-state branching processes. More
precisely, we define a growing family of discrete Galton-Watson trees with
i.i.d. exponential branch lengths that is consistent under Bernoulli
percolation on leaves; we define the Levy tree as the limit of this growing
family with respect to the Gromov-Hausdorff topology on metric spaces. This
elementary approach notably includes supercritical trees and does not make use
of the height process introduced by Le Gall and Le Jan to code the genealogy of
(sub)critical continuous-state branching processes. We construct the mass
measure of Levy trees and we give a decomposition along the ancestral subtree
of a Poisson sampling directed by the mass measure.
