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Grace Chisholm Young

The derivaties of real functions that Grace Chisholm Young studied, contributed to the formulations of the Denjoy-Young-Saks Theorem.  In multiple papers writen by Grace Chisholm Young and William Young, explains what the Denjoy-Young Saks Theorem is. William Young proved that if f is a continuous function, then f⁺(x) = f^–(x) and f_–(x) = f₊(x) everywhere except at a set of points of the first category. Then in one of Grace's paper she wrote the result that for an arbitrary function f, f⁺(x) ≥ f_–(x) and f^–(x) ≥ f₊(x) everywhere except at a countable set of points. 

http://www.agnesscott.edu/lriddle/women/abstracts/DYS_theorem.htm