Let Se be a countably family of in&rite subsets of nonnegative integers. Using a diagonal argumpnt it is straight forward to select for each XE& an infinite subset S(X) r~ X such that the family (S(X) 1 XE Se) is disjoint. Also, there exists a mapping A :N --, N such that for every XE & and i EN the
A remark concerning arithmetic progressions
✍ Scribed by József Beck
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 203 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0097-3165
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📜 SIMILAR VOLUMES
~roughout this paper we use the following notatians: The cardinality of the finite set Y is denoted by ISI -.s& B8, . I s den&e finite or infinite sets of positive integers. If & is a finite or infinite set of positive integers, then S(d) denotes the set of the distinct positive integers n that can
The study of the distribution of general multiplicative functions on arithmetic progressions is, largely, an open problem. We consider the simplest instance of this problem and establish an essentially the best possible result of the form where f is a nonnegative multiplicative function and (a, q)=