$\mathbb{E}[X^+]$ 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 $\mathbb{E}[X] = \mathbb{E}[-X] = 0, \mathbb{E}[X^2] > - \mathbb{E}[-X^2]$.

Integrating the equation $X = X^+ - X^-$ we get $E[X^+]=E[X^-]$.
