Almost Gibbsian versus weakly Gibbsian measures

We consider two possible extensions of the standard definition of Gibbs measures for lattice spin systems. When a random field has conditional distributions which are almost surely continuous (almost Gibbsian field), then there is a potential for that field which is almost surely summable (weakly Gibbsian field). This generalizes the standard Kozlov theorems. The converse is not true in general as is illustrated by counterexamples.Gibbs formalism Non-Gibbsian states