Accession Number : AD0428782

Title :   POINTWISE AND NORM CONVERGENCEOF DISTRIBUTIONS,

Corporate Author : ADELPHI UNIV GARDEN CITY NY

Personal Author(s) : Beltrami,Edward J.

Report Date : DEC 1963

Pagination or Media Count : 16

Abstract : Some results are derived concerning the relation between ordinary pointwise convergence, convergence in the sense of Schwartz distributions (weak convergence), and norm convergence of locally integrable functions by exploiting the notion of analytic continuation for distributions which was recently investigated by H. J. Bremermann and L. Durand III (Jour. Math. Phy. 1961). One of the results is that weak, normed, and almost everywhere pointwise convergence are the same for every dominated sequence provided a certain local equicontinuity in the mean condition is satisfied. A partial converse to this result, showing that norm convergence must imply the local equicontinuity condition and dominance as well as pointwise convergence for some subsequence, is also established. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, POTENTIAL THEORY), SEQUENCES(MATHEMATICS), FUNCTIONS(MATHEMATICS), TOPOLOGY, INTEGRALS, INEQUALITIES, MEASURE THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE