  The strongly intensive measures $\Delta[P_T,N]$ and $\Sigma[P_T,N]$ are used
to study the event-by-event fluctuations of the transverse momentum $P_T$ and
particle multiplicity $N$ in nucleus-nucleus collisions.
  A special normalization for these fluctuation measures ensures that they are
dimensionless and yields a common scale required for a quantitative comparison
of fluctuations. In this paper basic properties of the $\Delta[P_T, N]$ and
$\Sigma[P_T, N]$ measures are tested within different phenomenological models
using the Monte Carlo simulations (the so-called fast generators) and
analytical solutions. The obtained results are helpful to elucidate the
properties of $\Delta[P_T,N]$ and $\Sigma[P_T,N]$ measures.
