We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? We prove among others that the number of pieces is either at most 3 or uncountable, and we show that it is undecidable in and even ...
In the first part a general problem of decomposing Borel sets and functions into... SL Solecki - 《Journal of the American Mathematical Society》 被引量: 119发表: 1998年 Decomposing Baire Functions We discuss in the paper the following problem: Given a function in a given Baire class, into...
In fact, every set that is NP-hard under polynomial-time n/sup o(1/)-tt reductions is p-superterse unless P=NP. In particular no p-selective set is NP-hard under polynomial-time n/sup o(1/)-tt reductions unless P=NP. In addition, no easily countable set is NP-hard under Turing...
a>0, the closed set \{h\ge a\} does not contain 0 and hence it is bounded away from 0. Thus, \mu (\{ h\ge a\}) <\infty. Since \{h=t\} = t \cdot \{h=1\},\ t>0, the scaling property (2.2) of \mu implies that ...
We first prove Theorem 1.6 for simple sets, that is, the union of finitely many closed intervals. Let A⊂T be a simple set. Let c be the constant given by Proposition 3.2 and suppose that μ(2A)<c. Let p≥29 be a prime, that we will let tend to infinity ultimately. LetAp={j...
Let $\\R$ be a real closed field, $ {\\mathcal Q} \\subset \\R[Y_1,...,Y_\\ell,X_1,...,X_k], $ with $ \\deg_{Y}(Q) \\leq 2, \\deg_{X}(Q) \\leq d, Q \\in {\... S Basu,D Pasechnik,MF Roy - 《Journal of the European Mathematical Society》 被引量...
Under an Elsevier user license open archiveAbstract Let S be a subset of finite cyclic group Zn not containing the identity element 0 with S=−S. Cayley graphs on Zn with respect to S are called circulant graphs and denoted by Cay(Zn,S). In this paper, for connected non-complete circu...
Closed In order to do so, we are hoping you all could chime in on two design questions we have regarding your use cases: For technical reasons, it would allow us to ship this API more quickly if RWS storage only includes a select subset of JavaScript storage APIs and is transient. Below...
− 0 = 0 − ɛ,“0” is the standard part and “ɛ” is named the nonstandard part, where ɛ is closed to positive real number zero. In this case, the left and right endpoints of the nonstandard fuzzy membership values represent ambiguity and uncertainty while describing the ...
questions may induce social desirability bias and can present a reliability problem with open questions, as the wording used might have a different meaning for respondents10. In this case, the use of closed-ended questions and also to know the realities that respondents have to report are ...