The Companion Matrix and Its Properties
The Companion Matrix and Its Properties
复制标题
DOI：
10.1080/00029890.1964.11992294
复制
发表时间：
1964-06
影响因子：
0.5
通讯作者：
L. Brand
中科院分区：
文献类型：
--
作者：
L. Brand
如果 E 是闭集，则 E ('IC 和 f (E ('IC)) 也是闭集，因此如果 Eisa 是闭集的可数并集，则 f (E ('IC)) 是可测的。由于任何可测集都是一组测度为零的集和一个闭集可数并集的并集，所以现在足以证明当 E 的测度为零时 f (E ('IC) 是可测的，这立即从引理 5 得出。这完成了证明引理 6 的结论，定理 C 的结论也是如此。
If E is closed, so are E ('IC and f (E ('IC), and hence if Eisa countable union of closed sets, then f (E ('IC) is measurable. Since any measurable set is the union of a set of measure zero and a set which is a countable union of closed sets, it is now enough to prove thatf (E ('IC) is measurable when E is of measure zero, and this follows immediately from Lemma 5. This completes the proof of Lemma 6, and so also of Theorem C.