实验三 函数极限、导数与积分的计算 实验目的: 学习并掌握 Mathematica 中函数极限、导数、积分的计算方法,辅助相关课程的学习。 预备知识:
第 19 讲 Lebesgue 积分的极限定理
description
Transcript of 第 19 讲 Lebesgue 积分的极限定理
-
19 Lebesgue Riemann
-
19 Lebesgue
-
19 Lebesgue LeviE {fn} limEfn(x)dx =Elimfn(x)dx (1), {fn}Fatou Elimfn(x)dx limEfn(x)dx (2)
-
19 Lebesgue
1 { fn }
-
19 Lebesgue
-
19 Lebesgue {fn}(1)
2{fn} (1)
-
19 Lebesgue ELebesgue{ fn} ffELebesgue1
-
19 Lebesgue { fn }ELebesgue f>0 Nn>N |fn(x)-f(x)|< (xE) |fn(x)| < |f(x)|+ (xE) 3
-
19 Lebesgue E|f(x)|+ E3
-
Lebesgue Levi,{ } ,f:
-
19 Lebesgue 2 0 x(1/n,1) fn(x) = n x (0,1/n] (1)?
-
19 Lebesgue fn(x) 010 n 01 1 E{ fn}
-
19 Lebesgue {fn}E fEI {fn}EfIIELebesgueF n |fn(x)| F(x) a.e.[E]
-
19 Lebesgue
3III { fn } 1
-
19 Lebesgue E fnfEgoroff >0 EE am(E- E)< ; bfnEf lim E fn (x)dx = E limfn(x)dx (3)
-
19 Lebesgue E- E Riemannf[a,b], >0,>0[c,d][a,b]d-c<
-
19 Lebesgue E- E { fn } F E- E |fn(x)| dx E- EF(x)dx4 Riemann
-
19 Lebesgue 1Lebesgue
-
19 Lebesgue Ef(x)EL-|f(x)|EL-f(x)E f(x)
-
19 Lebesgue
-
19 Lebesgue
4f(x)E f(x)
-
19 Lebesgue
f(x)
-
19 Lebesgue N
EA
-
19 Lebesgue
f(x)
-
19 Lebesgue , :(Lebesgue){ }E FEL - (1). a.e.[E](2). a.e.[E]fE