THE DIFFERENCE AND RALATION BETWEEN RIEMANN CALCULUS AND LEBEGUE CALCULUS
ABSTRACT
This article begins from the fluxionary calculus developing process which draws out our have known Riemann integral calculus.Although the Riemann integral calculus theory is quite complete, when considered some questions, we saw the Riemann integral calculus very limit. To explain this question through the concrete examples.Therefore it is necessary to point out the Lebesgue integral calculus .which have the very superiority compared to the Riemann integral calculus. This article’s central task is to discuss and induce the difference and the relation between the Riemann integral calculus and Lebesgue integral calculus from what we have studied the knowledge about the two kinds calculus. Specifically comparing their definition, the existence of conditions, the nature of the Riemann calculus and Lebesgue calculus ,the Riemann integral calculus function class and Lebesgue integral calculus function class, as well as about the Riemann integral calculus and Lebesgue integral calculus there are some theorems. Furthermore through using the concrete example to explain Lebesgue integral calculus cause the question to be solved easily. Finally summarizing the two kinds integral calculus between the difference and the relation.By the way,Lebesgue integral calculus is Riemann integral calculus promotion,but It is not Riemann improper integral calculus promotion.