  The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of
the exponential function, an infinite-dimensional version of the fractional
Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)
:=E_{\alpha}(\int (e^{i\phi(x)}-1)d\mu (x)) \] which we prove to fulfill all
requirements of the Bochner-Minlos theorem.
  The identity of the support of this new measure with the support of the
infinite-dimensional Poisson measure ($\alpha =1$) allows the development of a
fractional infinite-dimensional analysis modeled on Poisson analysis through
the combinatorial harmonic analysis on configuration spaces. This setting
provides, in particular, explicit formulas for annihilation, creation, and
second quantization operators. In spite of the identity of the supports, the
fractional Poisson measure displays some noticeable differences in relation to
the Poisson measure, which may be physically quite significant.
