摘要:

Ifu2= ℵ2then the Martin‐Solovay tree constructs only countably many reals. This decides a number of open questions in descriptive set theory. For example: if there exists a measurable cardinal, then everyΣ31set with size bigger than ℵ1contains a perfect set; MA(ℵ1) plus sharps implies that everyΣ31set is Lebesgue measurable.

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.417

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

LetGbe a graph of order 2n+ l having maximum degree 2n− 1. We prove that the total chromatic number ofGis 2nif and only ife(G−w¯)+ α′(G−w¯)⩾n, wherewis a vertex of minimum degree inG,G−w¯is the complement ofG—w, e(G−w¯)is the size ofG−w¯, and α′(G−w¯)is the edge independence number ofG−w¯.

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.434

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.447

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.449

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.467

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.482

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We define a skew product entropy for conservative nonsingular transformations, show that it takes values in {0, ∞} and use it to distinguish two classes on nonsingular transformations. Binary and ternary type IIIλodometers have zero skew product entropy, while nonsingular K‐automorphisms have infinite skew product entropy.

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.497

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Two results are proved which show that a subharmonic function on the unit disc which does not grow too quickly and which does not have asymptotic value ∞ at too many points, must have finite minimal fine limits at boundary points forming a set of positive linear measure. Similar methods are used to obtain an asymptotic Phragmén‐Lindelöf theorem for subharmonic functions. These results generalize and improve on earlier results for holomorphic functions.

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.517

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.534

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We characterize the continuity of the topological entropy of bimodal maps of the interval and of the circle in terms of the behaviour of the iterates of the turning points and of the value of the topological entropy of the map under consideration. In the case of bimodal circle maps of degree one we also study the continuity of the entropy in terms of their rotation intervals.

ISSN:0024-6107    

DOI:10.1112/jlms/52.3.547

出版商:Oxford University Press    

年代:2016

数据来源: WILEY