On a Measure of Stochastic Dependence

An explicit expression is found for the amount of information (in the sense of A. N. Kolmogorov) about one $\sigma$-subalgebra contained in another $\sigma$-subalgebra of an abstract algebra with a probability measure. The formula obtained is generalized to a system of subalgebras of any cardinal number. The generalized quantity is a natural measure of the amount of stochastic dependence an such a system.