µ (X, F)

1, x0 " A,
(X, F) Ã F x0 " X µ(A) =
0, x0 " A.
/

X = N F = 2N µ(A) = 1
n"A

1
, #A < ",
n"A 2n
X = N F = 2N µ(A) =
", #A = ".

0, #A < ",
X = N F = 2N µ(A) =
", #A = ".

0, A ,
X = R F = B µ(A) =
", A .
µ Ã F X A, B, An " F n " N
A ‚" B Ò! µ(A) µ(B)
A ‚" B '" µ(B) < " Ò! µ(B\A) = µ(B) - µ(A)

" "

µ An µ(Ai)
n=1 n=1

"

A1 ‚" A2 ‚" . . . Ò! µ An = lim µ(An)
n"
n=1

"

µ(A1) < " '" A1 ƒ" A2 ƒ" . . . Ò! µ An = lim µ(An)
n"
n=1
µ Ã F X A, B, An " F n " N

"

µ(An) = 0 n " N Ò! µ An = 0
n=1
µ(B) = 0 '" A ‚" B Ò! µ(A) = 0
µ(B) = 0 Ò! µ(A *" B) = µ(A)
µ(B) = 0 Ò! µ(A\B) = µ(A)