Khrapchenko's classical lower bound $n^2$ on the formula size of the
parity function~$f$ can be interpreted as designing a suitable
measure of subrectangles of the combinatorial rectangle
$f^{-1}(0)\times f^{-1}(1)$. Trying to generalize this approach we
arrived at the concept of \emph{convex measures}. We prove the
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