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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具体确定了一类中心为二维的三步幂零李代数的导子代数，得到了导子代数的一些性质，并证明了这类幂零李代数是可完备化幂零李代数。

In this paper we explicitly determine the derivation algebras of a class of 3-step nilpotent Lie algebras, and obtain some properties of the derivation algebras.

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具体确定了一类中心为二维的三步幂零李代数的导子代数，得到了导子代数的一些性质，并证明了这类幂零李代数是可完备化幂零李代数。

In this paper we explicitly determine the derivation algebras of a class of 3-step nilpotent Lie algebras, and obtain some properties of the derivation algebras.

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