$\mathbb{E}[X^+]$ and $\mathbb{E}[X^-]$ I was wondering what is the relationship between $\mathbb{E}[X^+]$ and $\mathbb{E}[X^-]$, when $\mathbb{E}$ is a sublineair expectation and $\mathbb{E}[X] = \mathbb{E}[-X] = 0, \mathbb{E}[X^2] > - \mathbb{E}[-X^2]$.

Why do you get a different answer when you use:
\begin{eqnarray*}
\mathbb{E}[X^-] & = & \mathbb{E}[\max(-x,0)] \\
 & = & \int^{\infty}_{0} (-x) f(x) dx \\
 & = & - \mathbb{E}[X^+]
\end{eqnarray*}
