TD4. Mesure de Lebesgue

e
λRk∈R+µ
µ(A) = λ(kA)A
µ
A k ∈R+λ(kA) = kλ(A)
Rλ
{ei}i∈IR/Q
∀x∈R,∃!i∈I, x −ei∈Q.
ei[0,1[
[0,1[ ⊂[
a∈Q
−1<a<1
{a+ei, i ∈I} ⊂ [−1,2[ .
a6=b∈Q
{a+ei, i ∈I}∩{b+ei, i ∈I}=∅.
{a+ei, i ∈I}a∈Q−1< a < 1λ
R2B(R2) [a, b[×[c, d[
a, b, c, d ∈R, a ≤b, c ≤d
λ[a, b[×[c, d[= (b−a)(d−c).
R2
[a, b]×[c, d]a, b, c, d ∈R, a ≤b, c ≤d

R
R R R
Q R
U
A A U
K
A A K
ε > 0URε
(An)n∈NRAn
(Bn)n∈NRBn