Khrapchenko's classical lower bound n² on the formula size of the parity function f can be interpreted as designing a suitable measure of sub-rectangles of the combinatorial rectangle f^{- 1} (0) × f^{- 1} (1). Trying to generalize this approach we arrived at the concept of convex measures. We prove the negative result that convex measures are bounded by O (n²) and show that several measures considered for proving lower bounds on the formula size are convex. We also prove quadratic upper bounds on a class of measures that are not necessarily convex.