Khinchin's Theorem

Khinchin's Theorem states that for a broad class of random processes, the long-term average value they produce (like the average of a series over time) will almost surely approach a fixed number, called the expected value, assuming certain conditions are met. In simpler terms, if you observe a process enough over time, its average will stabilize around its average value, despite short-term fluctuations. This theorem helps ensure that time averages can reliably represent the true average behavior of complex stochastic systems, such as financial markets or physical phenomena, under suitable assumptions.