  A coding theorem and converse are proved for a large class of abstract
stationary channels with time structure including the result by Kadota and
Wyner (1972) on continuous-time real-valued channels as special cases. As main
contribution the coding theorem is proved for a significantly weaker condition
on the channel output memory - called total ergodicity w.r.t. finite alphabet
block-memoryless input sources - and under a crucial relaxation of the
measurability requirement for the channel. These improvements are achieved by
introducing a suitable characterization of information rate capacity. It is
shown that the $\psi$-mixing output memory condition used by Kadota and Wyner
is quite restrictive and excludes important channel models, in particular for
the class of Gaussian channels. In fact, it is proved that for Gaussian (e.g.,
fading or additive noise) channels the $\psi$-mixing condition is equivalent to
finite output memory. Further, it is demonstrated that the measurability
requirement of Kadota and Wyner is not satisfied for relevant continuous-time
channel models such as linear filters, whereas the condition used in this paper
is satisfied for these models. Moreover, a weak converse is derived for all
stationary channels with time structure. Intersymbol interference as well as
input constraints are taken into account in a general and flexible way,
including amplitude and average power constraints as special case. Formulated
in rigorous mathematical terms complete, explicit, and transparent proofs are
presented. As a side product a gap in the proof of Kadota and Wyner -
illustrated by a counterexample - is closed by providing a corrected proof of a
lemma on the monotonicity of some sequence of normalized mutual information
quantities. An abstract framework is established to treat discrete- and
continuous-time channels with memory and arbitrary alphabets in a unified way.
