AEP For Certain Continuous-time Stationary Ergodic Sources
Discrete-time functions can be interpolated to continuous-time functions. If such interpolation is measurable, we may define the continuous-time stationary process accordingly as . If AEP holds for the discrete-time process, as in the i.i.d. or finite-valued stationary ergodic cases shown above, it automatically holds for the continuous-time stationary process derived from it by some measurable interpolation. i.e. 
where corresponds to the degree of freedom in time . and are the entropy per unit time and per degree of freedom respectively, defined by Shannon.
An important class of such continuous-time stationary process is the bandlimited stationary ergodic process with the sample space being a subset of the continuous functions. AEP holds if the process is white, in which case the time samples are i.i.d., or there exists, where is the nominal bandwidth, such that the -spaced time samples take values in a finite set, in which case we have the discrete-time finite-valued stationary ergodic process.
Any time-invariant operations also preserves AEP, stationarity and ergodicity and we may easily turn a stationary process to non-stationary without losing AEP by nulling out a finite number of time samples in the process.
Read more about this topic: Asymptotic Equipartition Property
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