Characterization of the space of Riemann integrable functions by means of cuts of the space of continuous functions. Iстатья
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Аннотация:We consider the space RI of Riemann integrable functions and its relations (with respect to order cuts) with the space C of continuous bounded functions. It is proved that the Riemann completion C ↣ RI/ N , where N is the ideal of all sets of zero Jordan measure, is a more complicated analogue of the Dedekind completion ℚ ↣ ℝ when new additional structure on the spaces C and RI/ N called refinement is introduced. The proof is based on a new description of Riemann integrable functions differing from the description of Lebesgue-Vitali.