Where the last equality follows from the fact that " ? " has compact support, so is zero outside of a bounded set.
22.
For any nonempty compact set A in X . ( For contractive IFS this convergence takes place even for any nonempty closed bounded set A ).
23.
In addition, some texts require a polytope to be a bounded set, while others ( including this article ) allow polytopes to be unbounded.
24.
If \ R is viewed as a metric space, its open balls are the open bounded sets, and its closed balls are the closed bounded sets.
25.
If \ R is viewed as a metric space, its open balls are the open bounded sets, and its closed balls are the closed bounded sets.
26.
An indicator function of a bounded set is Riemann-integrable if and only if the set is measure-theoretically as the integral with respect to the Jordan measure.
27.
If it is a finite bounded set then it will have a minimum, but that's a fairly trivial statement so I wouldn't call it a theorem.
28.
They investigated what strategies the players should take given the constraints that they draw their strategies from computationally bounded sets and introduce grace periods to prevent the dominance of vengeful strategies.
29.
In finite-dimensional spaces, the Palais Smale condition for a continuously differentiable real-valued function is satisfied automatically for proper maps : functions which do not take unbounded sets into bounded sets.
30.
An intuitive reason why topological equivalence does not imply strong equivalence is that bounded sets under one metric are also bounded under a strongly equivalent metric, but not necessarily under a topologically equivalent metric.
