I was reading my notes and I was having trouble understanding theorem 4.3 below. I understand essentially what it is saying, but to me its simplying stating something rather intuitive? That given $\{C_n\}$ and $\{X_n\}$ then $\{C \bullet X\}$ is also a martingale. But how does it relate to the fact that "you cant beat the system"?
Martingale transform question
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