ON MONOTONE PRESENTATIONS OF BOREL SETS

Tamas Matrai; Miroslav Zeleny

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ON MONOTONE PRESENTATIONS OF BOREL SETS

机译：关于BOREL集的单调表示

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If A is a ∑_ξ~o set and A_n (n<ω) are Borel sets then we call {A_n : n < ω} a presentation of A if A = U_(n<ω) A_n and A_n (n < w) have lower Borel class than A has. We show that for 2 ≤ ε < ω_1 it is not possible to assign a presentation to ∑_ξ~o sets in a monotone way; i.e., it is not possible to define functions f_n: ∑_ξ~o → ∏_ξ~o (n < ω) such that for every A ∈ ∑_ε~o we have A = U_(n<ω) f_n(A) and A, A' ∈ ∑_ξ~o, A is contained in A' implies f_n(A) is contained in f_n(A') (n < ω). This answers a question of Marton Elekes in the negative. We also show the nonexistence of monotone presentation for Borel functions.

机译：如果A是一个∑_ξ〜o集，而A_n（n <ω）是Borel集，那么如果A = U_（n <ω）A_n和A_n（n

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《Real analysis exchange》 |2009年第2期|311-317|共7页
作者
Tamas Matrai; Miroslav Zeleny;
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Alfred Renyi Institute of Mathematics, Realtanoda Street 13-15, H-1053 Budapest, Hungary;

Charles University, Faculty of Mathematics and Physics,Department of Mathematical Analysis, Sokolovska 83, Prague 8, 186 75,Czech Republic;

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1. ON MONOTONE REPRESENTATIONS OF BOREL SETS [J] . Tamas Matrai Real analysis exchange . 2007,第report期

机译：关于BOREL集的单调表示
2. Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance [J] . Peter Jaeger Formalized Mathematics . 2014,第3期

机译：Borel集的事件，Borel集的构建和随机金融的随机变量
3. BOREL OD SETS OF REALS ARE OD-BOREL IN SOME SIMPLE MODELS [J] . Kanovei Vladimir, Lyubetsky Vassily Proceedings of the American Mathematical Society . 2019,第3期

机译：Borel OD集的真实套装是OD-BOREL在一些简单的型号中
4. 2 Irreducible modular representations of the Borel subgroup of GL_2(Q_p) [C] . Laurent Berger, Mathieu Vienney Symposium on Galois Representations and Automorphic Forms . 2014

机译：2 GL_2（Q_P）的BOREL子组的不可减少模块化表示
5. Integrable Representations for Equivariant Map Algebras Associated with Borel-de Siebenthal Pairs [D] . O'Dell, Matthew Tyler 2017

机译：与Borel-de Siebenthal对相关的等价映射代数的可积表示
6. Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization [O] . A. Cristofari, M. De Santis, S. Lucidi, 2018

机译：具有非单调线搜索以进行约束约束优化的有效集截断牛顿法的数据和性能
7. Every Borel function is monotone Borel [O] . Živaljević Boško 1991

机译：每个Borel函数都是单调的Borel

ON MONOTONE PRESENTATIONS OF BOREL SETS

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