- In mathematics, the
infimum (abbreviated inf;
plural infima) of a
subset S {\displaystyle S} of a
partially ordered set P {\displaystyle P} is the greatest...
- In mathematics, the
concepts of
essential infimum and
essential supremum are
related to the
notions of
infimum and supremum, but
adapted to
measure theory...
-
fashion for a
function (see
limit of a function). For a set, they are the
infimum and
supremum of the set's
limit points, respectively. In general, when...
- if a
sequence is
decreasing and is
bounded below by an
infimum, it will
converge to the
infimum. If a
sequence of real
numbers is
increasing and bounded...
-
unique supremum (also
called a
least upper bound or join) and a
unique infimum (also
called a
greatest lower bound or meet). An
example is
given by the...
-
bound is said to be a
tight lower bound, a
greatest lower bound, or an
infimum, if no
greater value is a
lower bound. An
upper bound u of a
subset S of...
- {\textstyle \bigvee S,} and similarly, the meet of S {\displaystyle S} is the
infimum (greatest
lower bound),
denoted ⋀ S . {\textstyle \bigwedge S.} In general...
-
points of a
metric space relative to the
intrinsic metric is
defined as the
infimum of the
lengths of all
paths from the
first point to the second. A metric...
- {\displaystyle C} ) and ‖ f ‖ ∞ {\displaystyle \|f\|_{\infty }} is
defined as the
infimum of
these bounds: ‖ f ‖ ∞ = def inf { C ∈ R ≥ 0 : | f ( s ) | ≤ C for...
-
limit infimum and
limit supremum of a set
sequence always exist and can be used to
determine convergence: the
limit exists if the
limit infimum and limit...
