勒贝格可测集和疏朗完备集是两类重要集合，是实变函数中的重要内容。

Lebesgue measurable set and the complete and nowhere dense set are two kinds of important set and are the important content in the real variable function.

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在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。

After constrcting the perfective space prove that this space is just the space of lebes gue integratiable function thus explain that lebes gue integral is the form of the perfective riemann integral.

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