In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By...

this paper has examined the phenomenon of convergence of per capita out put levels across the ic countries for the 1960-1998 periods. three concepts of convergence, i.e., sigma beta and relative beta, have been used. the estimated beta values reveals only a very weak convergence (?=.0014) across ic for 1960-1998 period. but when a more homogeneous group of countries were selected, the results s...