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The measure hypothesis is a quantitative strengthening of the P != NPconjecture which asserts that NP is a nonnegligible subset of EXP. Cai,Sivakumar, and Strauss (1997) showed that the analogue of this hypothesis in Pis false. In particular, they showed that NTIME[n^{1/11}] has measure 0 in P.We improve on their result to show that the class of all languages decidable innondeterministic sublinear time has measure 0 in P. Our result is based on DNFwidth and holds for all four major notions of measure on P.

Nondeterminisic Sublinear Time Has Measure 0 in P