Geodesic
Weaker forms of continuity and vector-valued Riemann integration
M. A. Sofi1
1 Department of Mathematics Kashmir University, Hazratbal Srinagar - 190 006 J & K, India
Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 1-6

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It was proved by Kadets that a weak$^{*}$-continuous function on $[0,1]$ taking values in the dual of a Banach space $X$ is Riemann-integrable precisely when $X$ is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.
DOI : 10.4064/cm129-1-1
Keywords: proved kadets weak * continuous function taking values dual banach space nbsp riemann integrable precisely finite dimensional note prove chet space analogue result showing riemann integrability holds exactly underlying chet space montel

M. A. Sofi 1

1 Department of Mathematics Kashmir University, Hazratbal Srinagar - 190 006 J & K, India 
@article{10_4064_cm129_1_1,
     author = {M. A. Sofi},
     title = {Weaker forms of continuity and vector-valued {Riemann} integration},
     journal = {Colloquium Mathematicum},
     pages = {1--6},
     publisher = {mathdoc},
     volume = {129},
     number = {1},
     year = {2012},
     doi = {10.4064/cm129-1-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm129-1-1/}
}
TY  - JOUR
AU  - M. A. Sofi
TI  - Weaker forms of continuity and vector-valued Riemann integration
JO  - Colloquium Mathematicum
PY  - 2012
SP  - 1
EP  - 6
VL  - 129
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm129-1-1/
DO  - 10.4064/cm129-1-1
LA  - en
ID  - 10_4064_cm129_1_1
ER  - 
%0 Journal Article
%A M. A. Sofi
%T Weaker forms of continuity and vector-valued Riemann integration
%J Colloquium Mathematicum
%D 2012
%P 1-6
%V 129
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm129-1-1/
%R 10.4064/cm129-1-1
%G en
%F 10_4064_cm129_1_1
M. A. Sofi. Weaker forms of continuity and vector-valued Riemann integration. Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 1-6. doi: 10.4064/cm129-1-1

Cité par Sources :