Fern\'andez R.
Measures for lattice systems
(93K, LATeX 2e)

ABSTRACT.  I review issues related with the presence or absence of 
Gibbsianness in measures describing random fields in lattices.
After a brief exposition of the definition and properties of Gibbs
measures, I discuss the phenomenon of non-Gibbsianness.  The
discussion involves three aspects: (1) Examples among renormalized
measures and invariant measures of stochastic transformations; (2)
probabilistic characterization of non-Gibbsian measures 
---lack of quasilocality and ``wrong'' large-deviation properties---,
and (3) proposed clasification schemes and notions of generalized
Gibbsianness.  The review closes with comments on directions for
further work.  [Contribution to the proceedings of Statphys 20]