A note on weak sequential convergence

Weak Sequential Convergence in L , ( p , X )

We provide some new results on the weak convergence of sequences or nets lying in L,((T, & r), X) = L,(p, X), 1 <p < co, i.e., the space of equivalence classes of X-valued (X is a Banach space) Bochner integrable functions on the finite measure space ( r, z, I”). Our theorems generalize in several directions recent resuls on weak sequential convergence in L,(p, X) obtained by M. A. Khan and M. ...

A note on convergence in fuzzy metric spaces

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

A note on weak dividing

We study the notion of weak dividing introduced by S. Shelah. In particular we prove that T is stable iff weak dividing is symmetric. In order to study simple theories Shelah originally defined weak dividing in [6] . This notion is overshadowed by that of dividing, as the first author proved that dividing is the right well-behaved notion for simple theories [2],[3],[5],and [4]. However Dolich’s...

A Note on Subseries Convergence

Convergence in a sequential two stages decision making process

We analyze a sequential decision making process, in which at each stepthe decision is made in two stages. In the rst stage a partially optimalaction is chosen, which allows the decision maker to learn how to improveit under the new environment. We show how inertia (cost of changing)may lead the process to converge to a routine where no further changesare made. We illustrate our scheme with some...