# 魏尔施特拉斯判别法

${\displaystyle \zeta (s)=\sum _{k=1}^{\infty }{\frac {1}{k^{s}}}}$

${\displaystyle |f_{n}(x)|\leq M_{n}}$

${\displaystyle \sum _{n=1}^{\infty }M_{n}}$

${\displaystyle \sum _{n=1}^{\infty }f_{n}(x)}$

${\displaystyle A}$一致收敛（常规意义下）。

${\displaystyle |f_{n}|\leq M_{n}}$

${\displaystyle ||f_{n}||\leq M_{n}}$,

## 参考文献

• Rudin, Walter. Functional Analysis. McGraw-Hill Science/Engineering/Math. January 1991. ISBN 0-07-054236-8.
• Rudin, Walter. Real and Complex Analysis. McGraw-Hill Science/Engineering/Math. May 1986. ISBN 0-07-054234-1.
• Whittaker and Watson (1927). A Course in Modern Analysis, fourth edition. Cambridge University Press, p. 49.