Weak variable-length source coding theorems

The author first defines a general source as an infinite sequence X={X/sup n/=(X/sub 1//sup (n)/,...,X/sub n//sup (n)/)}/sub n=1//sup /spl infin// of n-dimensional random variables X/sup n/ where each component random variable X/sub i//sup n/ (1/spl les/i/spl les/n) takes values in a countably infinite set /spl Xscr/ that is called the source alphabet. It should be noted that each component of X/sup n/ may change depending on block length n. This implies that the sequence X is quite general in the sense that it may not satisfy even the consistency condition as usual processes, where the consistency condition means that for any integers m,n such that m