单词 | equicontinuous |
释义 | > as lemmasequicontinuous equicontinuous adj. Brit. , U.S. , ΚΠ 1926 E. W. Hobson Theory of Functions of Real Variable (ed. 2) II. ii. 168 In case the family of continuous functions is such that, for each value of ε, a single set of sub-intervals or sub-cells can be so determined that, for every function f(x) of the family, the fluctuation in a sub-interval, or a sub-cell, of a set, is less than ε, the family is said to consist of equi-continuous functions. 1959 G. James & R. C. James Math. Dict. (ed. 2) 21/1 Ascoli's theorem. From any set of uniformly bounded functions equicontinuous on a bounded closed (compact) set (such as a closed interval) it is possible to select an infinite sequence which converges uniformly to a limit function which is also continuous. < as lemmas |
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