Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Minimal complementary sets

Author: Gerald Weinstein
Journal: Trans. Amer. Math. Soc. 212 (1975), 131-137
MSC: Primary 10J20
MathSciNet review: 0399023
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a group on which a measure m is defined. If $ A,B \subset G$ we define $ A \oplus B = C = \{ c\vert c = a + b,a \in A,b \in B\} $. By $ {A_k} \subset G$ we denote a subset of G consisting of k elements. Given $ {A_k}$ we define $ s({A_k}) = \inf m\{ B\vert B \subset G,{A_k} \oplus B = G\} $ and $ {c_k} = {\sup _{{A_k} \subset G}}s({A_k})$. Theorems 1, 2, and 3 deal with the problem of determining $ {c_k}$.

In the dual problem we are given B, $ m(B) > 0$, and required to find minimal A such that $ A \oplus B = G$ or, sometimes, $ m(A \oplus B) = m(G)$. Theorems 5 and 6 deal with this problem.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10J20

Retrieve articles in all journals with MSC: 10J20

Additional Information

Article copyright: © Copyright 1975 American Mathematical Society