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On the existence of $ω$@-primitives on arbitrary metric spaces

In: Mathematica Slovaca, vol. 53, no. 1
Janina Ewert - Stanislaw P. Ponomarev

Details:

Year, pages: 2003, 51 - 57
About article:
In this paper a final solution to the problem of the existence of $ω$@-primitives on an arbitrary metric space $(X,d)$ is given. Namely, it is shown that if $f:X\to [0,∞]$ is an upper semicontinuous function, vanishing at each isolated point of $X$, then there exists a function $F:X\to \Bbb R$ whose oscillation equals $f$ at each point of $X$. We call such a function $F$ an $ω$@-primitive for $f$. Moreover, an $ω$@-primitive can always be found in at most Baire class $2$.
How to cite:
ISO 690:
Ewert, J., Ponomarev, S. 2003. On the existence of $ω$@-primitives on arbitrary metric spaces. In Mathematica Slovaca, vol. 53, no.1, pp. 51-57. 0139-9918.

APA:
Ewert, J., Ponomarev, S. (2003). On the existence of $ω$@-primitives on arbitrary metric spaces. Mathematica Slovaca, 53(1), 51-57. 0139-9918.