  We investigate the measure problem in the framework of inflationary
cosmology. The measure of the history space is constructed and applied to
inflation models. Using this measure, it is shown that the probability for the
generalized single field slow roll inflation to last for $N$ e-folds is
suppressed by a factor $\exp(-3N)$, and the probability for the generalized
$n$-field slow roll inflation is suppressed by a much larger factor
$\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not
suffer from this difficulty.
