  Ergodic Functions are bounded uniformly continuous $(\text{BUC})$ functions
that are typical realizations of continuous stationary ergodic process. A
natural question is whether such functions are always the sum of an almost
periodic with an $L^1-$mean zero $\text{BUC}$ function. The paper answers this
question presenting a framework that can provide infinitely many ergodic
functions that are not almost periodic plus $L^1-$ mean zero.
