  The formalism allowing one to account for the effect of a finite space-time
extent of particle production region is given. Its applications to the lifetime
measurement of hadronic atoms produced by a high-energy beam in a thin target,
as well as to the femtoscopy techniques widely used to measure space-time
characteristics of the production processes, are discussed. Particularly, it is
found that the neglect of the finite-size effect on the pionium lifetime
measurement in the experiment DIRAC at CERN could lead to the lifetime
overestimation comparable with the 10% statistical error. The theoretical
systematic errors arising in the calculation of the finite-size effect due to
the neglect of non-equal emission times in the pair center-of-mass system, the
space-time coherence and the residual charge are shown to be negligible.
