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1、℄9BRFourierq4=F
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yG$A;R;'qSA4=F
yG$Ab
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yG$AbX$"C{9AS_
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2、S')uZ^:^:1.19U4XvFÆρa,XvFÆ~(i)ρ(x+y)≤ρ(x)+ρ(y);(ii)ρ(λx)=

3、λ

4、ρ(x),λ∈K.F{ρα,α∈A}a,yv(iii)ρα(

5、x)=0Svα∈Ab_x=0.^:1.29U4Xl℄yvF{ρα,α∈A}_Xa,B℄$4B℄$4l℄FÆ

6、

7、&luSvα∈A,ρα2

8、R?v

&l=FG$X'D_FA~CZ-{ρα,α∈A}7
A0F
y[A'{Nα1,...,αn(ǫ)

9、α1,...,αn∈A;ǫ>0,n∈N}.%Nα1,...,αn(ǫ)={x

10、ρα1(x)<ǫ,...,ραn(x)<ǫ}.x∈X,xF
y[A'{x+Nα1,...,αn(ǫ)

11、α1

12、,...,αn∈A;ǫ>0,n∈N}.2xβ→x<
7<ρα(xβ−x)→07α∈A)S℄=F
yG$'HausdorffG$^:1.3XyvF{ρα,α∈A}z{vB℄$4){xβ}a,Cauchy)qrq}α>0,α∈Al℄β0uρα(xβ−xγ)<ǫSβ,γ>β0bXa,(v}Cauchy)

13、℄XuS[jUgsTsA
^:1.4Tk&l4Xt&l4YvT(x0)=y0,Uy0℄Yu}XXV,l℄x0℄XuvXXUuT(U)

14、⊂V,_aT℄x0vR?CAZ-CD
bCA
yfYG$XAXCZ-{ρα,α∈A}{dβ,β∈B},9gX)A
ybC(9gB"12^1.1{ρα,α∈A}{dβ,β∈B}9U4XvT_3w3(a)dTw3(b)℄Æρα,α∈A℄d−

15、

16、&l3R?"℄Ædβ,β∈B℄ρ−

17、

18、&l3R?(c)}α∈A,l℄β1,···,βn∈B,C>0,u}x∈X,ρα(x)≤C(dβ1(x)+···+dβn(x)).6x}β∈B,l℄α

19、1,···,αm∈A,D>0,u}x∈X,dβ(x)≤C(ρα1(x)+···+ραm(x)).)k(a)⇒(b)B"A

yA
(b)⇒(c)α∈A}ραd
y[Tsρα(0)=0,2Nα(1),50Fd
y[ANβ1,...,βn(ǫ),β1,...,βn∈B,ǫ>0,!Nβ1,...,βn(ǫ)⊂Nα(1).

20、aρα_y=2dβ1(x)+···+dβn(x),dβi(y)≤ǫ/2<ǫ,i=1,···,n,2ρα(y)<1.2ρα(x)≤(dβ1(x)+···+dβn(x)).ǫT#0,u}x∈X,f(x)≤C(ρα1(x)+·

21、··+ραm(x)).%1
1.1A)kD
^1.3B℄$&l4X{ρα,α∈A}G{vY{dβ,β∈B}G{vTkXtYvFÆ5=_TR?veRD!7U}β∈B,l℄α1,···,αm∈A,C>0,u}x∈X,dβ(T(x))≤C(ρα1(x)+···+ραm(x)).3^:1.59U4X{ρα,α∈A}9vU}α,β∈A,l℄γ∈AC>0,uU}x∈X,ργ(x)≤C(ρα(x)+ρβ(x)).yoDfYG$X

22、Z-C{ρα,α∈A}'fAα1,···,αm∈A,5γ∈AC>0,!x∈X,γ(x)≤C(ρα1(x)+···+ραm(x)).(1.1B℄$&l4X9v{ρα,α∈A}G{v_f∈X∗w3Ul℄α∈A,C>0,u}x∈X,f(x)≤Cρα(x).$1.1}B℄$&l4Xl℄FÆWZw3vDS9vDUg//ZG$AaoTs[}Ay

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yG$}')S{)k}