We compute the effects induced by the use of
small CMB maps on the measurement of the
$\\cl{l}$ coefficients of the angular power spectrum
and show that small systematic effects have
to be taken into account.
We also compute numerically the cosmic variance and covariance
of the $\\cl{l}$ spectrum for various spherical cap like maps.
Comparisons with simulations are presented.
The calculations are done using the standard method based
on the spherical harmonic transform
or using the temperature angular correlation spectrum.
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