微積分的推廣，加減乘除的推廣，以及統計擬合

Abstract

我發現不同的平均型不等式可以嵌入到微積分裡，形成它們獨特的積分公式，微分公式，均值定理，泰勒展式，黎曼分割。以及離散統計量，連續統計量，範數皆可如此構造。平均型不等式、積分型算子、微分型算子、黎曼分割、離散統計量、連續統計量、範數這七種結構會形成一一對應關係。並且可以做維度的推廣。 第一部分描述嵌入可以形成微積分空間，第二部分描述第一部分可以自然誘導出加減乘除的推廣，第三部分描述一種新方法可以用作統計函數的擬合。

I found that inequalities can be embedded in Calculus to form their unique theorems such as its integration, differentiation, Mean-Value Theorem, Taylor Expansion, Riemann partition. And discrete statistics, continuous statistics and norms can also embedded. Average type inequalities, integration operators, differential operators, Riemann partitions , discrete statistics, continuous statistics ,and norms will have one-one onto correspondence. And it can have higher dimension extension. The first part states the embedding which forms Calculus space, the second part states the first part can naturally induce extension of addition, subtraction, multiplication, and division. And the third part states a method which can handle probability distribution fitting.