数学分析中，关于某个变量一致是什么意思？ 第1页

Roughly speaking, "uniform" means independent of some parameter. For example,

1. "A sequence of functions {f_n} (or a family of funtions {f_t: t in indexed set I}) is uniformly integrable" means there exists some constant C, independent of n or t repectively, s.t. (or , repectively) Hence here "uniform" means uniform in n (or t, as appropriate)
2. "a family of funtions {f_t: t in indexed set I}) converge uniformly to f" means the boundness estimate for |f_t(x)-f(x)| is independent of x. Hence here "uniform" means uniform in x.

In principle, uniform estimates allow us to do someting nice and fun, eg. interchanging limts, dropping one parameter by taking the limit sup/inf. It appears frequently in (real/harmonic) analysis.