MT/14. Martingale transform

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The fourteenth video of the online series for Martingale Theory with Applications at the School of Mathematics, University of Bristol.
  1. Marton Balazs UoB
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Best martingale series on whole of youtube...this is coming from a person who is very tightwad on praises...👍

quonxinquonyi
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Another conceptual question.., C_n is said to be predictable if C_n if F_{n-1} measurable. The idea of this definition is that when making decision/strategy, we have only info up to (n-1) and no idea what happens at time n (and perhaps beyond).
However, as we have filtration here, F_n is sigma-algebra in the increasing fashion in n. So if C_n is F_n measurable, it means C_n is F_{n+k} measurable as well for k=1, 2, 3, ... I then have a question:
In the definition of predictable/previsible random variable, is it OK that C_n take info up to a few steps before (n-1) but not really up to (n-1)? thanks!

texla-khqx