Rn
A ‚" Rn
A
µ > 0 G A ‚" G µ"(G\A) < µ
µ > 0 F F ‚" A µ"(A\F ) < µ
µ > 0 G F F ‚" A ‚" G µ"(G\F ) < µ
X = N µ" : 2X [0, "]
sup A + inf A
µ"(A) =
2
sup A - inf A
µ"(A) =
2
sup " = inf " = 0
0
2N µ" µ"(A) = sup A sup " = 0 µ"
{0} {1} µ"
X = {1, 2, 3} A = {{1}, {2, 3}, {1, 3}, "} f : A [0, "] f({1}) = 2
f({2, 3}) = 4 f({1, 3}) = 3 f({"}) = 0

" "

µ"(A) = inf f(An) : A ‚" An, An " A .
n=1 n=1
"
Fµ µ"
X = R A1 = {(a, b) : a, b " R} A2 = {(a, b] : a, b " R}
f1 : A1 [0, "], f1((a, b)) = b - a,
f2 : A2 [0, "], f2((a, b]) = b - a,
µ" µ" µ"(A) = µ"(A) A ‚" R
1 2 1 2
µ" X A, B ‚" X µ"(B) = 0 µ"(A *" B) =
µ"(A\B) = µ"(A)
 A, B ‚" X A )" B = " B µ"
"E‚"X µ"(E )" (A *" B)) = µ"(E )" A) + µ"(E )" B).
X = {1, 2, 3} A = {", {1}, {2, 3}}
f1(") = 0, f1({1}) = 0, f1({2, 3}) = a > 0,
f2(") = 0, f2({1}) = b > 0, f2({2, 3}) = 0.
" "
µ" µ" Fµ = Fµ
1 2
1 2