LM-积分收敛定理的推广

Generalization of the LM-integral Convergence Theorem

在Riemann积分定义及其改进定义、δ-精细分法、δ-精细M-分法和ULSRS定义的基础上,分析了δ-精细分法的产生原理,分析了Lebesgue积分和Mcshane积分的等价性质.对L-积分的收敛定理给予了推广,建立了定理3,该定理优于L-收敛定理.

Based on Riemann integral definition and its improved definition, δ- elaborate partitioning method , δ- elaborate M-partitioning method and ULSRS definition, this paper analyzes the principle of generation of δ-elaborate partitioning method, and the equivalence properties of Lebesgue integral and Mcshane integral. And then the L-integral convergence theorem is generalized and, theorem 3 is established. This theorem is superior to L-convergence theorem.