Infinite determinantal measures

Infinite determinantal measures introduced in this note areinductive limits of determinantal measures on an exhaustingfamily of subsets of the phase space. Alternatively,an infinite determinantal measure can be describedas a product of a determinantal point processand a convergent, but not integrable, multiplicative functional.    Theorem 4.1, the main result announced in this note, gives an explicit description forthe ergodic decomposition of infinite Pickrell measures on thespaces of infinite complex matrices in terms of infinitedeterminantal measures obtained by finite-rank perturbations ofBessel point processes.