Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Does bounded almost surely imply bounded in Lp?

**Physics Forums | Science Articles, Homework Help, Discussion**