The following is an exercise from Bruckner's Real Analysis:
(a) : The other three definitions are in Wiki.
(b) : $D^+f=0$, $D_-f=0$, $D_+f=-\infty$ and $D^-f=\infty$.
(c) : ?
(d) : By considering $h=\frac{1}{n}$, $\liminf$ and $\limsup$ of measurable functions are measurable?
I cannot find a solution for (c) ; and am I correct about (b) and (d)?