1) Of a sampling process 2) Random 3) Statistically expected 1) Random 
The property of a dynamical system such that all regions of a phase space are visited with similar frequency and that all regions will be revisited (within a small proximity) if given enough time.
Informally: a stochastic process is ergodic if no sample helps meaningfully to predict values that are very far away in time from that sample. Another way to say that is that the time path of the stochastic process is not sensitive to initial conditions. Two events A and B (e.g. possible sets of states of the process) are ergodic iff, taking the li...
pertaining to a random function the temporal mean values of which are identical to the corresponding statistical mean values
The property of a dynamical system such that all regions of a state space are visited with similar frequency and that all regions will be revisited (within a small proximity) if given enough time. 
<radiobiology> A mathematical term meaning space-filling. If a magnetic field is ergodic, any field line will eventually pass arbitrarily close to any point in space. Closely related to chaotic. ... (09 Oct 1997) ... 
A more precise formulation of the concept of randomness. With an ergodic series of data there is no memory, no correlation with past data, so each new data point adds the same amount of new information.
System or process in which the final state is independent of the initial state.
adjective positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions
of or pertaining to the condition that, in an interval of sufficient duration, a system will return to states that are closely similar to previous ones: the assumption of such a condition underlies statistical methods used in modern dynamics and atomic theory.