f : (X, F) R = [-", "]
a " R f-1((-", a))
a " R f-1((-", a])
a " R f-1((a, "))
a " R f-1([a, "))
f : (X, F) R
f-1([a, b]), f-1((a, b]), f-1([a, b)), f-1((a, b))
a, b " R a < b
f, g : (X, F) R
{x : f(x) < g(x)} , {x : f(x) g(x)} , {x : f(x) = g(x)} , {x : f(x) = g(x)} .

f : (X, F) R B " F
f|B
f, g : (X, F) R
 " R f
f + g f - g
fg
min{f, g} max{f, g}
f : (X, F) R f(x) = c c " R
A ‚" X

1, x " A,
:
1A(x) =
0, x " A
/
A
 1A*"B = 1A + 1B - 1A)"B
1A)"B = 1A1B
Ã
f : R R x " R
f : R R f2
f : X R f(x) = 1A(x) - 1B(x) A, B " F
f

Ã(f) = Ã( f-1(B) : B " B )
f : R R f(x) = sgn x Ã(f)
f, g : [0, ") [0, ")
" "

f(x) = n1[2n,2n+2)(x), g(x) = 1[2n,")(x).
n=0 n=0
Ã(f) ‚" Ã(g) Ã(g) ‚" Ã(f)
f, g : R R


1
f(x) = sin(Ä„x) , g(x) = sgn sin(Ä„x) .
2
Ã(f) ‚" Ã(g) Ã(g) ‚" Ã(f)
f, g : [0, ") [0, ")

"

x2, x " N,
f(x) = n1[n,n+1)(x), g(x) =
x + 1 x , x " N.
/
n=0
Ã(f) ‚" Ã(g) Ã(g) ‚" Ã(f)
f, g : [0, ") R

"

x(x + 1), x " N0,
f(x) = n1(n,n+1](x), g(x) =
x + 1 2, x " N0.
/
n=0
Ã(f) ‚" Ã(g) Ã(g) ‚" Ã(f)
 f, g : [0, ") [0, ")
" "

f(x) = n1[n,n+1)(x), g(x) = n1[2n (x).
-1,2n+1-1)
n=0 n=0
Ã(f) ‚" Ã(g) Ã(g) ‚" Ã(f)
"
f : [0, ") [0, ") f(x) = x g : [0, ") [0, ") g(x) = x
Ã(f)
f : [0, ") R f(x) = 2 · x à Ã(f) Ã({[0, n) : n " N})
à Ã( x3 ) Ã( x )