Geodesic
On family of subspaces of the space of regulated functions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2009), pp. 7-24

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In the space of regulated functions the parametrical family of subspaces of special kind is investigated. Subspace crossing representing them is investigated too. It includes the space of functions of bounded variation. The lattice of subspaces depending from parameter is investigated. Questions of existence of integral Riemann–Stieltjes for elements of subspaces are investigated. Completeness of subspaces is proved (for everyone subspace own norm is used). Relations between norms are investigated.
Keywords: regulated function, Riemann–Stieltjes integral, Banach algebra. 
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     author = {V. I. Rodionov},
     title = {On family of subspaces of the space of regulated functions},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {7--24},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_4_a1/}
}
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V. I. Rodionov. On family of subspaces of the space of regulated functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2009), pp. 7-24. http://geodesic.mathdoc.fr/item/VUU_2009_4_a1/