- exists. If the
supremum of S {\displaystyle S} exists, it is unique, and if b is an
upper bound of S {\displaystyle S} , then the
supremum of S {\displaystyle...
-
lower limit, or
inner limit;
limit superior is also
known as
supremum limit,
limit supremum, limsup,
superior limit,
upper limit, or
outer limit. The limit...
-
concepts of
essential infimum and
essential supremum are
related to the
notions of
infimum and
supremum, but
adapted to
measure theory and functional...
- \right\}.} This norm is also
called the
supremum norm, the
Chebyshev norm, the
infinity norm, or, when the
supremum is in fact the maximum, the max norm...
- mathematics, the least-upper-bound
property (sometimes
called completeness,
supremum property or l.u.b. property) is a
fundamental property of the real numbers...
- {\displaystyle S} of a
partially ordered set P {\displaystyle P} is the
supremum (least
upper bound) of S , {\displaystyle S,}
denoted ⋁ S , {\textstyle...
-
directed subset D of P with
supremum in P, its
image has a
supremum in Q, and that
supremum is the
image of the
supremum of D, i.e. ⊔ f [ D ] = f ( ⊔...
- {\displaystyle K} ,
which in turn
implies that f {\displaystyle f}
attains its
supremum and
infimum on any (nonempty)
compact set K {\displaystyle K} . Thus, we...
- a_{2}\leq a_{3}\leq ...\leq K}
converges to its
smallest upper bound, its
supremum. Likewise, a non-increasing bounded-below
sequence converges to its largest...
- or infima.
Roughly speaking,
these functions map the
supremum/infimum of a set to the
supremum/infimum of the
image of the set.
Depending on the type...
