勒贝格积分与积分变换公式

Lebesgue integral and integral transformation formula

目的为了减弱面积变换公式和二重积分变换公式成立的条件。方法利用勒贝格积分和傅立叶级数讨论平面区域面积变换公式和二重积分变量变换公式。结果在比现有文献有关结论中较弱条件下得到了面积变换公式和二重积分的变量变换公式。结论对现有的有关面积变换公式和二重积分变量变换公式的结果作了相应的改进和推广。

Aim To weaken conditions on＇transformation formula of area and doubly integration. Methods By using Lebesgue integral and Fouries series, area transformation formula of planar domain and variant transformation formula of double integral are discussed. Results Under some wea- ker conditions the area transformation formula of planar domain and variant transformation formula of double integral are obtained. Conclusion Some well-known results on area transformation formula and variant transformation formula of double integral are improved and generalized.