The zero-one law holds for BPP

@article{Melkebeek2000TheZL,
  title={The zero-one law holds for BPP},
  author={Dieter van Melkebeek},
  journal={Theor. Comput. Sci.},
  year={2000},
  volume={244},
  pages={283-288}
}
We show that BPP has p-measure zero if and only if BPP differs from EXP. The same holds when we replace BPP by any complexity class C that contains BPP and is closed under tt-reductions. The zero-one law for each of these classes C follows: Within EXP, C has either measure zero or else measure one. 

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