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Every local martingale (Yn) can be represented as a martingale transform (Cn)•(Xn) of some martingale

This is from the following lecture notes https://qmplus.qmul.ac.uk/pluginfile.php/2479408/mod_resource/content/3/L3-2020.pdf Theorem 3.12.

Is this true? I don't see any other math resources that state this fact. Further, I am not sure how to prove this seemingly easy result. I found that this is related to "predictable representation property" in Brownian motion, but I haven't learned that far yet. Can you give me some insight?

jk001
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    Pls refer to P. A. Meyer，"Martingales and Stochastic Integrals I", Lecture Notes in Mathematics No.284, Springer-Verlag(1972). Th.II.42, p.47. – JGWang Dec 04 '21 at 08:44
  • Thanks for your response. I wonder why this is not as well-known? – jk001 Dec 07 '21 at 15:52

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