The topology of the weak dual Ks′Ω (which is quasi-complete by Theorem 3.102, since KΩ is barreled) is known as the vague topology. (V) Real Radon measures and positive Radon measures Write KℝΩ for the set of real continuous functions on Ω. The subset K+Ω formed by the φ...
the very first ever—based on a novel particle interpretation for this evolution. The classical particle interpretation for the heat flow in an open setYwith Dirichlet boundary condition is based on particles which move around inYand are killed (or lose their mass) as soon...
A non-zero measure visa tangent measure of μ at a if there are positive sequences ri→ 0 and ci such that ci Ta.riμ→ v in the vague topology. Tangent measures have been used to great effect in relating local features of a measure to properties such as integral dimensionality and ...
ln 3 l i lnY f 3 lY f for all f P g Rd and wpH Rd be the space of ®nite mea- sures over Rd endowed with the topology of vague convergence, i.e., the topology in which, ln 3 l i lnY f 3 lY f for all ...
Rough set theory was also studied from topological view by Skowron [23] and Wiweger [27]. Then, many authors investigated some applications of rough set and topology on incomplete and vague things and explored further important structures; see, for example, [15], [20], [22]. On the ...
Another characterization of vague convergence is by means of Lipschitz functions. Let E be a Polish space endowed with a boundedness{\mathscr{B}}. We say that a metricdon a Polish space is compatible with{\mathscr{B}}ifdinduces the topology of E and for everyB\in {\mathscr{B}}there exi...