Kolmogorov consistency conditions

Kolmogorov consistency conditions

[‚kȯl·mə′gȯ·rȯf kən′sis·tən·sē kən‚dish·ənz]
(mathematics)
For each finite subset F of the real numbers or integers, let PF denote a probability measure defined on the Borel subsets of the cartesian product of k (F) copies of the real line indexed by elements in F, where k (F) denotes the number of elements in F ; the family {PF } of measures satisfy the Kolmogorov consistency conditions if given any two finite sets F1 and F2 with F1 contained in F2, the restriction of PF2to those sets which are independent of the coordinates in F2 which are not in F1 coincides with PF1.