As I know, Shannon-McMillan-Breiman Theorem holds for stationary and ergodic discrete-valued random varialbes, and AEP for continuous-valued random varialbes only holds when the source is an i.i.d. source. What about the continuous-valued stationary and ergodic? What is the condition for $\lim_{n\to\infty} \log\frac{1}{P(U^n)} \to c$, where $c$ is some constant? For example, power-limited source, or the limit $\lim_{n\to\infty}\frac{H(U^n)}{n}$ exists?
2026-03-28 14:53:43.1774709623
SMB Theorem/AEP for stationary and ergodic continuous-valued process
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