ISSN:0025-5793    

DOI:10.1112/S0025579300012201

出版商:London Mathematical Society    

年代:1982

数据来源: WILEY

摘要:

AbstractLetGbe a locally compact abelian group. Then there is a finitely additive regular set functionmdefined on an algebraAof Borel sets inG,m(G) = 1, such thatm(T‐1F) =m(F) for allF∈Aand all surjective group endomorphismsTofGontoG.

ISSN:0025-5793    

DOI:10.1112/S0025579300012213

出版商:London Mathematical Society    

年代:1982

数据来源: WILEY

摘要:

AbstractFor a convex polytopeP, lets(P) and σ(P) denote, respectively, the largesttsuch thatPhas at‐dimensional face (section) which is a simplex. Using Gale diagrams, lower bounds are obtained for these numbers and formulae are developed for the behaviour of s and σ over Cartesian and other products.

ISSN:0025-5793    

DOI:10.1112/S0025579300012225

出版商:London Mathematical Society    

年代:1982

数据来源: WILEY

摘要:

AbstractLet ℱ denote a set of subsets ofX= {1, 2,…, n). Let deg(i) be the number of members of ℱ containingiand val(ℱ) = min {deg (i):i∈X). Suppose nokmembers of ℱ have unionX. We conjecture val(ℱ) ≤ 2n‐k‐1fork≥ 3. This is known for n ≤ 2k and we prove it fork≥ 25. Fork= 2 an example has val(ℱ)>2n‐2(l−n‐0·651) and we prove val(ℱ) ≤ 2n‐2(1–n‐1). We also prove that if the union ofksets one from each of ℱ1,…, ℱkhas cardinality at mostn – tthen min {cardinality ℱj}<2nαtwhere αk= 2α − 1 and ½<α<1.

ISSN:0025-5793    

DOI:10.1112/S0025579300012237

出版商:London Mathematical Society    

年代:1982

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300012249

出版商:London Mathematical Society    

年代:1982

数据来源: WILEY