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Lutz's resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , resource bounded measure gives a method to classify the size of subsets of complexity classes.
For instance, computer scientists generally believe that the complexity class P is not equal to the complexity class NP. Since P is a subset of NP, this would mean that NP contains more problems than P. A stronger hypothesis than "P is not NP" is the statement "NP does not have p-measure 0". Here, p-measure is a generalization of Lebesgue measure to subsets of the complexity class E, in which P is contained. P is known to have p-measure 0, and so the hypothesis "NP does not have p-measure 0" would imply not only that NP and P are unequal, but that NP is, in a measure-theoretic sense, "much bigger than P".