In
mathematics, the Denjoy–Luzin theorem, introduced independently by and
states that if a
trigonometric series
In mathematics, a trigonometric series is a infinite series of the form
: \frac+\displaystyle\sum_^(A_ \cos + B_ \sin),
an infinite version of a trigonometric polynomial.
It is called the Fourier series of the integrable function f if the term ...
converges absolutely on a set of positive measure, then the sum of its
coefficients
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...
converges absolutely, and in particular the trigonometric series converges absolutely everywhere.
References
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Fourier series
Theorems in analysis
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