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I am a bit confused by the concept of "bounded almost surely".

If a random variable [tex]X(\omega)[/tex] is bounded a.s., so this means (i) [tex] X \leq K [/tex] for some constant [tex] K [/tex] ? or some [tex] K(\omega) [/tex]?

Also, if it is bounded almost surely, does that mean it is also bounded in [tex] L^{p} [/tex]? Apparently if case (i) is true, then it should be also bounded in [tex] L^{p} [/tex]?

Thanks.

Wayne

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# Does bounded almost surely imply bounded in Lp?

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