For example , a Fourier series of sine and cosine functions , all continuous , may converge pointwise to a discontinuous function such as a step function .
There are many counterexamples using the standard definition of pointwise convergence .
A Fourier series of sine and cosine functions , all continuous , may converge pointwise to a discontinuous function such as a step function .
There are many counterexamples using the standard definition of pointwise convergence .