what does Xn mean here?

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Yes Xn is a sequence. Your other post uses the same variable, so let us say that the converging sequence is Yn instead of Xn; then if you have a set of random variables X1...Xn, Yn = -1/n*log(p(X1...Xn)), and this Yn converges in probability to H(X) (as N->infinity, Pr(|Yn-H(X)|>epsilon)->0).
 

would not we use X^n instead of Xn to represent a sequence?

How is X^n differ from Xn?

I always confused about this
 

X^n and Xn are just notation. Different people and different books use different notation; you have to pay attention to the context to see which one is being used.
 

In my textbook, the author use both.

This involves a problem that Xn may refer to X1 X2, which are the symbol in the sequence.

Shug said:
X^n and Xn are just notation. Different people and different books use different notation; you have to pay attention to the context to see which one is being used.
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