Measure theory and weak König's lemma
Measure theory and weak König's lemma
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测度论和弱 König 引理
DOI：
10.1007/bf01621469
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发表时间：
1990
影响因子：
0.3
通讯作者：
S. G. Simpson
中科院分区：
文献类型：
--
作者：
Xiaokang Yu;S. G. Simpson
在具有限制归纳法的二阶算法子系统的背景下，我们发展了测度理论。我们引入了一个组合原理wwkl （weak-weak König’s引理），并证明了它严格弱于wkl （weak König’s引理）。我们证明了wwkl等价于勒贝格测度在开集上是可数可加性的表述的一个正式版本。我们还证明了wwkl等价于紧度量空间上的任何Borel度量在开集上是可数可加的陈述的形式版本。
We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive on open sets.