Positive projections and conditional mathematical expectations

One indicates how to construct the reduction of an arbitrary positive projection in to a strictly positive one and one proves that the latter is almost the operator of the conditional mathematical expectation relative to some -sub-algebra. More exactly, one shows a method of selecting from a strictly positive projection an operator of conditional mathematical expectation type (this concept is introduced in the paper).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 47, pp. 172–174, 1974.