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A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...
Maximum point-blank range is principally a function of a cartridge's external ballistics and target size: high-velocity rounds have long point-blank ranges, while slow rounds have much shorter point-blank ranges. Target size determines how far above and below the line of sight a projectile's trajectory may deviate.
A set with an upper (respectively, lower) bound is said to be bounded from above or majorized [1] (respectively bounded from below or minorized) by that bound. The terms bounded above ( bounded below ) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.
A locally bounded TVS is a TVS that possesses a bounded neighborhood of the origin. By Kolmogorov's normability criterion , this is true of a locally convex space if and only if the topology of the TVS is induced by some seminorm .
In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; in particular, every local martingale that is bounded from below is a supermartingale, and every local martingale that is bounded from above is a submartingale; however, a local ...
The metric space (M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets of R n the two are equivalent. A metric space is compact if and only if it is complete and totally bounded. A subset of Euclidean space R n is compact if and only if it is closed and
Baker Mayfield has made big plays for the Buccaneers all season. None quite like this. The Tampa Bay quarterback, who threw a career-best 41 touchdowns during the regular season, got the job done ...
Each set has a supremum (infimum), if it is bounded from above (below). Proof: Without loss of generality one can look at a set A ⊂ R {\displaystyle A\subset \mathbb {R} } that has an upper bound. One can now construct a sequence ( I n ) n ∈ N {\displaystyle (I_{n})_{n\in \mathbb {N} }} of nested intervals I n = [ a n , b n ] {\displaystyle ...