MathDB
Miklos Schweitzer 1962_5

Source:

September 18, 2008
functioncalculusderivativereal analysisreal analysis unsolved

Problem Statement

Let f f be a finite real function of one variable. Let D‾f \overline{D}f and D‾f \underline{D}f 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 D‾f \overline{D}f and D‾f \underline{D}f are Borel-measurable functions. [A. Csaszar]
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