On a problem of Bruckner and Ceder concerning the sum of Darboux functions
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- by J. S. Lipiński PDF
- Proc. Amer. Math. Soc. 62 (1977), 57-61 Request permission
Abstract:
The main purpose of this paper is to show that for some continuous function f and any preassigned, countable and dense set D of real numbers there exists a measurable function d which takes on every real value in every interval such that the range of $f + d$ is D.References
- A. M. Bruckner and J. Ceder, On the sum of Darboux functions, Proc. Amer. Math. Soc. 51 (1975), 97–102. MR 387507, DOI 10.1090/S0002-9939-1975-0387507-6
- K. M. Garg, Monotonicity, continuity and levels of Darboux functions, Colloq. Math. 28 (1973), 91–103, 162. MR 323964, DOI 10.4064/cm-28-1-91-103
- J. S. Lipiński, On level sets of Darboux functions, Fund. Math. 86 (1974), 193–199. MR 357702, DOI 10.4064/fm-86-2-193-199
- Avadhesh Narayan Singh, On some new types of non-differentiable functions, Ann. of Math. (2) 28 (1926/27), no. 1-4, 472–476. MR 1502799, DOI 10.2307/1968391
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 57-61
- MSC: Primary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0425037-5
- MathSciNet review: 0425037