Expectation of little o in probablity - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-25T09:57:45Z http://mathoverflow.net/feeds/question/85414 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85414/expectation-of-little-o-in-probablity Expectation of little o in probablity maikol.solis.chacon 2012-01-11T13:40:55Z 2012-01-25T16:22:12Z <p>If I have $Z=o_p(1)$ where $o_p$ is the little-o in probability. I'm interested in find some properties about $E(Z)$.</p> <p>My first idea was</p> <p>$E(Z)=E(Z (1_{Z>\varepsilon} + 1_{Z\leq\varepsilon}) ) \leq E(Z^2)P(Z>\varepsilon) +\varepsilon P(Z\leq\varepsilon)$,</p> <p>for some $\varepsilon > 0$. </p> <p>As you can see, it's required that $E(Z^2)&lt;\infty$ and it don't seems like an appropriate condition.</p> <p>So my philosophical question is: Can we give to $E(Z)$ any sense? </p> <p>Regards. </p> http://mathoverflow.net/questions/85414/expectation-of-little-o-in-probablity/85417#85417 Answer by Tom Ellis for Expectation of little o in probablity Tom Ellis 2012-01-11T14:36:06Z 2012-01-11T14:36:06Z <p>It may help to consider the indicators of the intervals [0,n] on the probability space [0,1] with Lebesgue measure.</p>