论文标题
在密集地说明点上使用任意阳性衍生物提高奇异函数
Increasing singular functions with arbitrary positive derivatives at densely lying points
论文作者
论文摘要
令A为任意可计数的真实集，例如a = q。令g为从a到正实数的任意映射，例如g（a）= 2^a。 我们展示了如何构建严格增加的实际函数f，以使得几乎所有实数x的a and f'（x）= 0中的每个x的f'（x）= g（x）。
Let A be an arbitrary countable set of reals, for example A=Q. Let g be an arbitrary mapping from A into the positive reals, for example g(a)=2^a. We show how a strictly increasing real function f can be constructed such that f'(x)=g(x) for every x in the set A and f'(x)=0 for almost all real numbers x.
