Let $f$ be a distributionally chaotic map of the interval such that the endpoints of the minimal periodic portions of any basic set are periodic. Then the principal measure of chaos, $\mu _p(f)$, is not greater than twice the spectral measure of chaos $\mu _s(f)$. This proves an assertion of Schweizer et al. in a special case.
"On measures of chaos for distributionally chaotic maps.." Real Anal. Exchange 32 (1) 213 - 220, 2006/2007.