منابع مشابه
Generalized Rings of Measurable and Continuous Functions
This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
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We investigate some problems of the following type: For which sets H is it true that if f is in a given class F of periodic functions and the difference functions ∆hf(x) = f(x + h) − f(x) are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by H(F ,G), that is, H(F ,G) = {H ⊂ R/Z : (∃f ∈ F \ G) (∀h ∈ H) ∆hf ∈ G}, we try to charact...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0335728-x