Geodesic
The $R_F$-convergence and theorems of Banach Steinhauss type
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 1, pp. 47-67

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The concepts of $R_F$-convergence in the space of real (or complex) functions over a Hausdorff topological space and of Riemann integrable functions without using the Riemann integral are given. Some properties of $R_F$-convergence and theorems of Banach Steinhauss type have been proved. 
@article{FPM_1997_3_1_a3,
     author = {J. L. Fernandez Muniz and L. Alvarez Marin},
     title = {The $R_F$-convergence and theorems of {Banach} {Steinhauss} type},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {47--67},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a3/}
}
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J. L. Fernandez Muniz; L. Alvarez Marin. The $R_F$-convergence and theorems of Banach Steinhauss type. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 1, pp. 47-67. http://geodesic.mathdoc.fr/item/FPM_1997_3_1_a3/