Unbounded divergence of Fourier series of continuous functions

For any given set E ⊂ [0, 2π), of measure zero, a function f(t) ε C (0, 2π), is constructed whose Fourier series is unboundedly divergent on E. If E is closed, there is a function φ{symbol}(t) ε C (0, 2π), whose Fourier series diverges unboundedly on E and converges on [0, 2π)E. © 1970 Consultants Bureau.