Unformatted text preview: n
E Ui . i=1 Then P1 and P2 are plurirectangles, P1 ) Sf ) P2 and
measN +1 P2 ' measN +1 P1 =
= n
+ measN +1 Ui ' i=1
n
+,
i=1 n
+ measN +1 Ti i=1 n
+,
sup f ' 0 measN Ri '
inf f ' 0 measN Ri
Ri i=1 ( Ri ( = U (f, P ) ' L (f, P ) % (. It follows from Theorem 137 that the set Sf is Peano—Jordan measurable with
A
measN +1 Sf =
f (x) dx.
R Conversely, assume that the set Sf is Peano—Jordan measurable. Let R 1 [0, M ]
be a rectangle containing Sf . Then /Sf is Riemannintegrable over R 1 [0, M ]
with
A
measN +1 Sf =
/Sf (x, y ) d (x, y ) .
R For every x ! R, the function...
View
Full Document
 Spring '14
 Trigraph, Ri, measure, Lebesgue integration, Meas

Click to edit the document details