  We provide extension procedures for nonlinear expectations to the space of
all bounded measurable functions. We first discuss a maximal extension for
convex expectations which have a representation in terms of finitely additive
measures. One of the main results of this paper is an extension procedure for
convex expectations which are continuous from above and therefore admit a
representation in terms of countably additive measures. This can be seen as a
nonlinear version of the Daniell-Stone theorem. From this, we deduce a robust
Kolmogorov extension theorem which is then used to extend nonlinear kernels to
an infinite dimensional path space. We then apply this theorem to construct
nonlinear Markov processes with a given family of nonlinear transition kernels.
