- 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...
- {\displaystyle X\to Y} then H {\displaystyle H} is
equicontinuous if and only if it is
equicontinuous at the origin; that is, if and only if for
every neighborhood...
- 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...
- {\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...
-
equicontinuous subset of X ′ {\displaystyle X'} is weak-*
compact and
equicontinuous and furthermore, the
convex balanced hull of an
equicontinuous subset...
- 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...
- discontinuity, discontinuous, entertain, entertainment, equicontinuity,
equicontinuous, impertinence, impertinent, incontinence, incontinent, intenible, intercontinental...
- 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...
