Measure Theory

Camillo
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 .

Risposte
Camillo
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 $ .

Chevtchenko
As you surely know, there are several ways in which to define the Lebesgue measure. Which one do you want me to apply?

Camillo
Obviously correct, show it applying the definition :D

Chevtchenko
It is 0, of course. :D

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