  It was shown many times in the literature that a Markov random field is
equivalent to a Gibbs random field when all realizations of the field have
non-zero probabilities; the proofs are rather complicated. A simpler proof,
which is based directly on simple probability theory, is presented.
Furthermore, it is shown that the equivalence is still valid when there are
constraints (zero probability realizations) of any type. The equivalence
extends to infinite size random fields, as well.
