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oo p+q+r~-- k-+oo 1, (1) where k is the number of the trial, then P = PPa + qPb + rPc, q ----Pq~ + qqb + rqc, (2) r = pr a -[- qrb + rrc. The system (2) is linearly dependent; it has a unique solution (and, consequently, the chain possesses an ergodic property) if and only if the determinant of the system composed of any two equations (2) and equation (1) does not vanish.

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LINNIK. Leningrad, 1951. In Russian. Note. Apart from entries published after 1951, the bibliography of MARKOV'Sworks [47, pp. 679-714] fails to mention items [1; 35; 36; 14]. In addition, the information provided under items [9] and [16] re the difference between the translations of MARKOV'S contributions and their Russian originals or about the very existence of German versions of some of MARKOV'S articles is lacking in the bibliography. Finally, the bibliography supplied an unsuitable title for booklet [11] which was published as a manuscript withe ut any title at all.

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A. A. Markovs work on probability by Sheynin O. B.


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