# A convergence theorem for the improper Riemann integral of Banach space-valued functions

@article{Escamilla2014ACT, title={A convergence theorem for the improper Riemann integral of Banach space-valued functions}, author={J. A. Escamilla and M. Raggi and Luis Angel Gutierrez and F. Hern{\'a}ndez}, journal={International Journal of Mathematical Analysis}, year={2014}, volume={8}, pages={2451-2460} }

In this paper, we establish a characterization, by means of the uniform convergence, of a convergence which is based in the Moore’s ideas [4]; then, according to this characterization, we give a convergence theorem for the improper Riemann integral of functions taking values in a Banach space. Mathematics Subject Classification: 28B05, 46G12

#### References

SHOWING 1-10 OF 11 REFERENCES

The multidimensional fundamental theorem of calculus

- Mathematics
- 1987

On compact oriented differentiable manifolds, we define a well behaved Riemann type integral which coincides with the Lebesgue integral on nonnegative functions, and such that the exterior derivative… Expand

The topology of close approximation

- Mathematics
- 1990

Abstract Three topologies on function spaces are considered; in increasing order of fineness they are: convergence in measure, uniform and “close approximation”. For simplicity and definiteness,… Expand

The Elements of Real Analysis

- Mathematics, Computer Science
- 1964

A Glimpse at Set Theory: The Topology of Cartesian Spaces and the Functions of One Variable. Expand

Expressing measurable functions by one-one ones

- Mathematics
- 1982

Let .;rP be a u-field of subsets of a set X, with a countable separating system; typically X could be the real line R, and .D the family .9(R) of Bore1 sets, or of all Lebesgue measurable sets.… Expand

Intregrales Vectoriales de Riemann y McShane

- Intregrales Vectoriales de Riemann y McShane
- 2002

La m-Topologa en Espacios de Funciones, Master Thesis

- La m-Topologa en Espacios de Funciones, Master Thesis
- 1998

The Elements of Real Analysis, John Wiley and Sons, Inc

- United States of America,
- 1964