Let f be a finite real function of one variable. Let Df and Df be its upper and lower derivatives, respectively, that is, \overline{D}f\equal{}\limsup_{{h,k\rightarrow 0}_{{h,k \geq 0}_{h\plus{}k>0}}} \frac{f(x\plus{}h)\minus{}f(x\minus{}k)}{h\plus{}k} ,
\underline{D}f\equal{}\liminf_{{h,k\rightarrow 0}_{{h,k \geq 0}_{h\plus{}k>0}}} \frac{f(x\plus{}h)\minus{}f(x\minus{}k)}{h\plus{}k}. Show that Df and Df are Borel-measurable functions. [A. Csaszar] functioncalculusderivativereal analysisreal analysis unsolved