Definition of Equicontinuous. Meaning of Equicontinuous. Synonyms of Equicontinuous

- In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood...
- must be independent of n and x.) The sequence is said to be uniformly equicontinuous if, for every ε > 0, there exists a δ > 0 such that | f n ( x ) − f...
- the same as that of the proof that a pointwise convergent sequence of equicontinuous functions on a compact set converges to a continuous function. By uniform...
- equicontinuous subset of X ′ {\displaystyle X'} is weak-* compact and equicontinuous and furthermore, the convex balanced hull of an equicontinuous subset...
- {\displaystyle 0} in X; If H is an equicontinuous subset of X ′ {\displaystyle X'} then the following sets are also equicontinuous: the weak-* closure, the balanced...
- every weakly bounded countable union of equicontinuous subsets of its continuous dual space is again equicontinuous. This property is a generalization of...
- L(X;Y)} is equicontinuous. For any F-space Y {\displaystyle Y} every pointwise bounded subset of L ( X ; Y ) {\displaystyle L(X;Y)} is equicontinuous. An F-space...
- generally, a set of functions with bounded Lipschitz constant forms an equicontinuous set. The Arzelà–Ascoli theorem implies that if {fn} is a uniformly bounded...
- strongly bounded countable union of equicontinuous subsets of its continuous dual space is again equicontinuous. This property is a generalization of...
- the topology of pointwise convergence. If E {\displaystyle E} is an equicontinuous subset of L ( Y ; Z ) {\displaystyle L(Y;Z)} then the restriction C...