  A word-valued source $\mathbf{Y} = Y_1,Y_2,...$ is discrete random process
that is formed by sequentially encoding the symbols of a random process
$\mathbf{X} = X_1,X_2,...$ with codewords from a codebook $\mathscr{C}$. These
processes appear frequently in information theory (in particular, in the
analysis of source-coding algorithms), so it is of interest to give conditions
on $\mathbf{X}$ and $\mathscr{C}$ for which $\mathbf{Y}$ will satisfy an
ergodic theorem and possess an Asymptotic Equipartition Property (AEP). In this
correspondence, we prove the following: (1) if $\mathbf{X}$ is asymptotically
mean stationary, then $\mathbf{Y}$ will satisfy a pointwise ergodic theorem and
possess an AEP; and, (2) if the codebook $\mathscr{C}$ is prefix-free, then the
entropy rate of $\mathbf{Y}$ is equal to the entropy rate of $\mathbf{X}$
normalized by the average codeword length.
