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On a Paper by M. Iosifescu and S. Marcus

  • C. J. Neugebauer

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In this paper we will construct an example showing that the problem posed in [1] has a negative answer. Two more theorems on the subject treated in [1] will be included.

Let Io = [0, 1], R the reals, and let, for A ⊂ R, Ao be the interior of A. Let {xn} be a sequence in [0, 1> such that 0 = x1 < x2 < … and lim xn = 1. For each n, let In be closed interval having x as its midpoint (except for n = 1 in which case x1 is the left endpoint of I1) such that In ∩ Im= ϕ, and the metric density relative to Io of at 1 is zero. Let Jn be a closed interval in In concentric with In (except for n = 1, where J1 has x1 as its left endpoint) whose length is half that of In

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References

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1. Iosifescu, M. and Marcus, S., Sur un problème de P. Scherk concernant la somme de carrés de deux dériées, Canad. Math. Bull. vol. 5, no. 2 (1962), pp. 129-132.
2. Saks, S., Theory of the Integral, Warszawa-Lwow, 1937.
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On a Paper by M. Iosifescu and S. Marcus

  • C. J. Neugebauer

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