CantorLebesgue
The Cantor-Lebesgue theorem is a fundamental result in real analysis concerning the behavior of trigonometric series. It states that if a trigonometric series converges to a function $f(x)$ almost everywhere on a set $E$ with positive Lebesgue measure, and if the coefficients of the series tend to zero, then the function $f(x)$ is Lebesgue integrable on $E$. Furthermore, the integral of $f(x)$ over $E$ can be expressed in terms of the Fourier coefficients.
More formally, consider a trigonometric series of the form $\frac{a_0}{2} + \sum_{n=1}^\infty (a_n \cos(nx) + b_n \sin(nx))$. If
A significant consequence of the Cantor-Lebesgue theorem is that if a trigonometric series converges everywhere to