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There are many research works devoted to Gibbs measure for models on Cayleytrees. Among these works, there are some works in which the general results areidentical, but the considered models are various. In this article, we presentthe construction of Gibbs measures in the language of measure theory and replyto the question ``When can we construct Gibbs specifications?" Also, we presenta new condition (convenient for verification) which is equivalent to theconsistency condition of kernels. The obtained results in the article aregeneral, not for a particular model. On the contrary, these results hold forsome considered models on Cayley trees.

Gibbs measures on spatial systems on vertices of Cayley trees