Measure theory and weak König’s lemma. (English) Zbl 0718.03043
The authors study measure theory in the context of subsystems of second order arithmetic and reverse mathematics. They show that a formal statement of countable additivity for Lebesgue measure is equivalent to \(WKL_ 0\) over \(RCA_ 0\). They extend this result to arbitrary Borel measures on compact metric spaces.
Reviewer: S.G.Simpson
MSC:
| 03F35 | Second- and higher-order arithmetic and fragments |
Keywords:
measure theory; subsystems of second order arithmetic; reverse mathematics; countable additivity; Lebesgue measure; Borel measuresReferences:
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