黎曼_勒贝格引理的推广.pdf
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17 4 Vol17N o. 4
2002 8 J ournal of Leshan T eachers College A ug2002
( 乐山师范学院数学系, 四川乐山6 14004
: L2 .
: ; ; L 2 ;
: O172 . 2 : A : 1009 8666( 2002 04 0019- 0 3
: f( x , :
b b
lim f ( x cosx dx= 0 lim f( x sinxdx = 0
+ a + a
b T b
1
: lim f ( x f( x dx= g ( x dx f( x dx
+ a T 0 a
( g ( x T 0
L2 . :
2 2
: f L [ a, b] , g T 0 , g L [ 0, T ] ,
b T b
1
lim f ( x f( x dx= g( x dx f ( x dx
+ a T 0 a
:
1 f [ a, b] , g [ 0, T ] .
T
g ( x T 0, g( x , f ( x [ a, b] , 0,
0, [ a, b] :
a= x 0 x1 x2 xn- 1 xn = b
k = [ x k- 1 , xk ] , xk = xk - xk- 1 , ( k= 1, 2, , n
max x , x, x , | f ( x - f( x |
k k
,
b T b
1
f( x g( x dx- g ( x dx f( x dx
a T 0 a
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