Note that for abelian von Neumann algebras acting on such direct integral spaces, the equivalence of the weak operator topology, the ultraweak topology and the weak * topology on norm bounded sets still hold.
32.
X ^ \ star is defined as the space of continuous linear functionls X'endowed with the topology of uniform convergence on totally bounded sets in X ( and the " stereotype second dual space"
33.
:and it's easy to see that this limit is uniform only if x is constrained to be in some bounded set .-- Talk ) 07 : 01, 5 February 2006 ( UTC)
34.
The famous Mandelbrot set is a subset of this parameter space, consisting of the points in the complex plane which give a bounded set of numbers when a particular iterated function is repeatedly applied from that starting point.
35.
So { "'L " "'k " } is a bounded set in the Banach space of operators, therefore relatively compact ( because the underlying vector space is finite-dimensional ).
36.
Is it correct to say, for a bounded set, that to find the average value of a function over that set, just integrate over that set and divide by its Lebesgue measure, assuming that its Lebesgue measure is nonzero?
37.
If in addition " B " is stable under the formation of convex hulls ( i . e . the convex hull of a bounded set is bounded ) then " B " is called a "'convex vector bornology " '.
38.
Is there a term for / area of study of the type of bounded sets ( specifically in \ mathbb { R } ^ n ) such that x \ in U \, \ Rightarrow-x \ in U ? ( Where U also contains 0 ).
39.
X ^ \ star is defined as the space of all linear continuous functionals f : X \ to \ mathbb { C } endowed with the topology of uniform convergence on totally bounded sets in " X ", and the " second dual space"
40.
In geometry, the "'Chebyshev center "'of a bounded set Q having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q, or alternatively ( and non-equivalently ) the center of largest inscribed ball of Q.
