Measure Theory
Let $ E sub RR^2 $ be the set formed by the circumferences with centre in the origin and radius $r = 1/n $ ($ n$ integer $> 0 $ .
Let calculate the Lebesgue measure of E, $ m(E) $ according to the definition .
Let calculate the Lebesgue measure of E, $ m(E) $ according to the definition .
Risposte
A subset $ A sube RR^n$ has zero Lebesgue measure when $AA epsilon > 0 $ , exists a sequence $ [R_k ]$ of rectangles such that :
$A sube uu_(k=0)^oo R_k $ and $ sum_(k=0) ^oo |R_k | <= epsilon $ .
$A sube uu_(k=0)^oo R_k $ and $ sum_(k=0) ^oo |R_k | <= epsilon $ .
As you surely know, there are several ways in which to define the Lebesgue measure. Which one do you want me to apply?
Obviously correct, show it applying the definition

It is 0, of course.
