Can somebody explain why a non-negative local submartingale of the class DL is a submartingale? I was reading the proof here https://almostsure.wordpress.com/2009/12/24/local-martingales/ in Lemmma 3 but I dont understandd why can we take the limits inside the cconditional expectation usingg the uniform integrrability property!
2026-02-22 23:10:59.1771801859
A non-negative local submartingale of the class DL is a submartingale
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