Definition:Median of Continuous Random Variable/Warning

Median of Continuous Random Variable: Warning
Care should be directed towards the uniqueness of medians.

For example, if $\map {f_X} x = 0$ on some closed real interval $\closedint a b$ of $x$, we may have $\ds \int_{-\infty}^{m_X} \map {f_X} x \rd x = \frac 1 2$ for all $m_X \in \closedint a b$.