THEOREM 4: The function f^2 is Lipschitzian but not differentiable at the points of the set {(1/2)*[m - sqrt(d)]: m is an integer and there exists an integer n such that d = m^2 - 4n is positive but not a perfect square} . [This set is dense in the reals.]
THEOREM 5: If g is a function discontinuous at the rationals and continuous at the irrationals, then there is a dense uncountable subset of the reals at each point of which g fails to satisfy a Lipschitz condition.
かな？
特に、THEOREM 5 変形トマエ函数（Ruler Function）のような、有理数で不連続、無理数で連続なる函数では、 ”there is a dense uncountable subset of the reals at each point of which g fails to satisfy a Lipschitz condition.” だと
