几个实值函数可积充要条件的p-adic类似

研究了p-adic数域上实值函数可积的充要条件．在引入与实分析类似的幅度概念之后，证明了区间[ap,bp]上有界实值函数f（x）可积的几个充分必要条件：（1）当λ→0时，S和S同时收敛于同一极限I；（2）Aεp，σp，可找到δp，使任意分法满足λ（Δ）=maxΔ1≤i≤n〈δp时，对应于幅度ωi≥εp的那些区间Δl的长度之和∑i=1nΔi〈σp；（3）若f（x），g（x）在[ap,bp]可积，f（x）·g（x）在[ap，bp]也可积．并分析了实数域与p-adic数域上可积充要条件表述及证明方法的异同．

Several real-valued function's integral necessary and sufficient condition of p-adic similarity

The necessary and sufficient condition of real-valued function is researched in p-adic fields. After giving amplitude which is similar to real analogy, the necessary and sufficient condition of real-valued function f（x） is proved completely, that is （1） when λ→0, S and s converged same limit I at the same time; （2） for Aεp, and σp,δp can be found, make ∑i=1nΔi〈σp when interal Δl satisfy ωi≥εp for any partitions λ（Δ）=maxΔ1≤i≤n〈δp ;（3） if f（x）,g（x） integrated on [ap ,bp],f（x）·g（x） could integrated on [ap ,bp] too. The difference between p-adic field and real number field on expression and proof method are compared.