More can be concluded by applying the principle of condensation of singularities.
2.
Such reasoning leads to the "'principle of condensation of singularities "', which can be formulated as follows:
3.
The principle of condensation of singularities then says that the set of continuous functions whose Fourier series diverges at each " x m " is dense in C ( \ mathbb { T } ) ( however, the Fourier series of a continuous function " f " converges to " f " ( " x " ) for almost every x \ in \ mathbb { T }, by Carleson's theorem ).
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