MASS PROBLEMS AND MEASURE-THEORETIC REGULARITY

被引：6
|
作者：
Simpson, Stephen G. [1 ]
机构：
[1] Penn State Univ, Dept Math, State Coll, PA 16802 USA
来源：
BULLETIN OF SYMBOLIC LOGIC | 2009年 / 15卷 / 04期
关键词：
measure theory; Borel sets; hyperarithmetical hierarchy; Turing degrees; Muchnik degrees; LR-reducibility; reverse mathematics; EVERYWHERE; MEDVEDEV;
D O I：
10.2178/bsl/1255526079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F-sigma set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility We build some omega-models of RCA(0) which are relevant for the reverse mathematics of measure-theoretic regularity.
引用
收藏
页码：385 / 409
页数：25
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