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We study discontinuity of the Lyapunov exponent. We construct alimit-periodic Schr\"odinger operator, of which the Lyapunov exponent has apositive measure set of discontinuities. We also show that the limit-periodicpotentials, whose Lyapunov exponent is discontinuous, are dense in the space oflimit-periodic potentials.

Discontinuity of the Lyapunov Exponent