Consider the functions
where , , each is an arbitrary number, and has period one. We show that there is a constant such that if b is large enough, then the Hausdorff dimension of the graph of is bounded below by . We also show that if a function f is convex Lipschitz of order , then the graph of f has - finite measure with respect to Hausdorff’s measure in dimension . The convex Lipschitz functions of order include Zygmund’s class . Our analysis shows that the graph of the classical van der Waerden-Takagi nowhere differentiable function has -finite measure with respect to .