  I address some recently raised issues regarding the time-parametrization
dependence in stochastic descriptions of eternal inflation. To clarify the role
of the choice of the time gauge, I show examples of gauge-dependent as well as
gauge-independent statements about physical observables in eternally inflating
spacetimes. In particular, the relative abundance of thermalized and inflating
regions is highly gauge-dependent. The unbounded growth of the 3-volume of the
inflating regions is found in certain time gauges, such as the proper time or
the scale factor gauge. Yet in the same spacetimes there exist time foliations
with a finite and monotonically decreasing 3-volume, which I demonstrate by an
explicit construction. I also show that there exists no "correct" choice of the
time gauge that would yield an unbiased stationary probability distribution for
observables in thermalized regions.
