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flOKASATE/lbCTBO. Hepea \M\M oSoanaHaTb MoniHOCTt, MHO-

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ripeflCTaanaiouieH (JiyHKuneil MHOJKecTBa HaaoaeM iJiyHKiiHio, pasnyio O

Ha MHowecrse H / BHG ero.

OnpenenHM MHOwecTBO & aanaHKeM ero npencTasnaiomeft <JiyHKiiHH;t:

O6 OaHOMeCTHblX np-:MiiTitBHO pSKypCKBHMX 4'Y H K U U 8 X 85

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=. ^ j j £ | c e a & t < .r J. I ^ j •{ r I (3-i)f,:\

cjiyiao,

rae oc - MHOMSCTBO H3 /le.MMt! 4.

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ecna

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ne nepecexaeTca c HHM, TO

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, HSM HpHMOli H6~

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pOClfiT CX B 3TOft TOHK6.

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^ "HHTepBany*, coaepKameMy <7 : npHnnmeM HOMep

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na* c HOMepoM jc ).

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HOMep HSKOTOporo 'HHTepeana*.

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cocTOHmeft us MHO%ecfB /^^ H yaoBnerBopaiouiefl (2) , B aononneHHH K

'"**HMeexcs 6ecKOHeiHO MHOPO "KycKOB* MHOwecTBa PQ HJIH 6ecxoHeHHO

MHOrO 'KyCKOB* MHOJKeCTBa PQ .

flpyrHMH cnosaMH, B nonojiHeHHH K U*< HMeerca SecKOHSHHO MHOPO

nepecHfix UK B 6ecKOHeiHOM HHcne xoieK He

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THBHO pexypcHBHofi ijiyHKiiHeft ( B CHny Bw6opa oc. ).

TEOPEMA 2 . A n r e 6 p a P o 6 H H c o H a H w e e x

K O H T H H y y M M a K C H M a j i b H U x n o a a n r e 6 p .

flOKA3ATE;i bCTBO. DycTb &cx) - yKaaaHHaa B jjl] 4>yHKUHa, 06-

paayiomaa onHosneMSHTHbifl 6aanc anreSpu PoSHHcona.

flna KajKfloro MHOwecTBa p!** HS neMMbi 5 onpenejiHM

jio)ft

MHO^cecTBy M HarypanbHtix HHCB/I nocxaBHM B cooTBercT-

BHG cHcreMy <J>yHKunfl

B CHny Bbi6opa P. *'npu KarcnoM M SM ynoanerBopaex

( A ) , nosTOMy 5^ xo«e ynoBnerBopaex (A) H, cnenosaxenbHo, HS coBnaaa-

ST co Bceft anre6pofi.

O6 OAHOMeCTHblX npHMHTHBHO DeXypCHBHMX forHKIIBM 87

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pa BxnroqaeTca B HexoTOpyio MaxcHManbHyro noaanreflpy._ rt fgl

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^ ^ J>o°) s<*>ManbHaa noaanreopa conepwana OBI npn HeKoxopoM L a. . wjC. , oua^ yf°;, y7^ -coaepxana OH f^ -t-fa=aeu, cneaoBarenbHo, coBnaaana OH co Bceft an -

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TaxHM o6pa3OM, ana paaHux A/ MaKCHMajibHbie noaanreSpbi, BKJIIO-

iaiomne S.. » pasnHHHti.wTeopeMa noKasaaa.

3.TEOPEMA 3 . C y m e C T B y e r H P H M H T H B H O

p e x y p c H B H a a (fi y H K n H a , K o T o p a fl, H B -

n a a c b H r e p a u H e f t H e x o T o p o f t 4> y H K -

U H H , H e f l B J i f l e r c a H r e p a u n e f t K H K B —

K o f t o 6 i n e p e K y p c H B H o f l i J i y H K U H H .

AOKA3ATE/lbCTBO. FlycTb oc0 H/30 ~ peKypcuBHo nepenncnHMbie

peKypCHBHo HeoxnenHMbie MHOMcecTsa, cx=pc/.z:=.=?yf-/ , TAB yecx0 I ,

y3 = {je|.or=v>y4-/ , me ^£yS0j.

a: yi j3 xaioKe pexypciiBHo nepeHHcnHMw H peKypcuBHo HeoxaenH-

K<bi (rax K3K ecna 6u oc OTnenanocb or e peKypcHBHHM MHo»cecTBOM

9 , Toac0 ornenanocfa 6bi ofj30 peKypCHBHWM MHOJKOCTBOM -|,x|

rne ^ey H y Heierno 1 .

IlycTb cffjc) H tT(x) - npHMHTHBHO peKypcHBHbie (jiyHKUHH, nepe -

awmHe oc H 0 cooTBeTCTBeHHO.

OnpeaenHM fyymtuiuo 9(-x:l '•

f <-*(u) , ecnu x=4ujr1 K

J <J(y) , ecjiH jr=4yh3 H

\ - B ocranfaHfaix cnyiaax.

npHMHTHBHO peicypCHBHa, npH pasHbix -x. npHHHMaer paanwe

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aa oc H A , cocToamne H3 HenerHbix nncen); 0(01 = 0 ; <y npHHHMaer

B xaqecTBe 3na«ieHHJl Bee incna H3occ/y3 . ECJIH <y(jc)e.ct. , tocr(x-'r-f)

BHfl 8u+-4- ; ecnn a(sc)e.& , TO &(jc+f) HMBBT Ban Su .

aanaerca HTepauneft (})yHKUHH

88 B.B.KoabMHHbix

(a raKxe nio6oro e& pacuiHpeHHa) .

/Iro6aa 4>yHKUHH, HrepauHS Koropoft pasna Q- , scrb paciuiipeuHe ' •£.

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.

EcnH 6bi c: 6una Brepaunefi

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or ^ peKypcHBHHM MHOjKecTBOM jc| (^u^Cfa (x)= &eJ+4-)^ . Ho a: n /9

peicypcHBHO HeoraenHMbi.

TEOPEMA 4 . C y m e c T B y e x H P H M H T H B H O

p e x y p c H B H a f l 1̂ 1 y H K u H H , B a a H M H o o a~

H o s H a M H O O T o S p a M c a w m a a H a r y p a n b

H b i f t p a n H a c e 6 a , K O T O p a H , a u . T a a c b

H r e p a u H e f t H e K o r o p o f i <)i y H x u H H , He « B -

n a e T C H H r e p a u H e f t H H K a x o f t n p H M H

T H B H O p S K y p C H B H O f l 4 > y H K 1 I H H -

flOKASATE/lbCTBO. CymecrsyeT HPHMHTUBHO peicypcHBHaH fyyux. -

una a0czc') , saanMHO onHosnaHHO oroepawaiouiaa HarypanbHtift paa Ha

ce6a H Taxaa, HTO G^(x) ne flBnaerca HPHMHTHBHO peicypcHBHoft [61 .

OnpeaenHM Q (x) CXSMOH:

X HfeTHOM,

X H6H6THOM.

npHMHTHBflo peKypciiBHa, BaaHMHo oflHoaHaHHO OTo6pa>KaeT Hary -

pan Ha ce6a; &co)=- O . &(xj nansieTcsi HTepauneft (

f 2<y 6- )-t-/nP« x iSTHOM,> = J >;i^i/\f%o(

, oqeBHflHo, raxaa -f-

Ecnn 6bi f(x) 6bina HPHMHTHBBO peKypCHBHa, TO , B CHJTJ pasencT-

Ba

jr.t \- [

OS OAHOMeCXHblX npHMHTHBHO peKypCHBHblX $y HKIIHHX 89

6bi xaK>Ke ITPHMHXHBHO peKypciiBHa, HTO npoxnBopennT BW-

TeopeMa flOKaaaua.

4. OnpeaeniiM onepaumo "xoHHoro o6pameHHH" cneny»mnM oopaaotvi:

ecnH &(x) BaaiiMHo oflHoanaHHo oTo6pa>KaeT HaxypanfaHbiii pan na ce6a,

sxa onepauHH craBHT efi & cooTBercrBue (J'yHKU1110 T (-D > B nporHB -

HOM cjiyiae 3ra onepauns HenpiiMeHHMa K f(x) .

3AME4AHME 2. Ha (jsyHKuafi ±(x) H <7(x) onepauHSMH •* , -+- H

"TOHHOTO o6pameHHa" HeBO3MO>i<no nonyiHTfa see oaHOMecTHue o6mepeKyp-

CHBHbie (})yHKUHH.

fleiScTBHTent-HO, Ha -arax asyx ^yHKKHfl onepauHHMH ^- H 4- Kent. -

aa nonymTb (JjyHKUHio, aaaiiMHO oflHO3nanHO oToSpaxaroiuyio

psia Ha ce6s (H, cnenoBatenbHo, oiiepauHH ''TOHHOTO oSpameHHSj"

lecKH He yqacTsyer B nonyieHHH HOBBIX

3ro BbixeKaeT HS cnenyioinero

/Iio6aH (J'yHKiiHfl ^t , nonyieHHaH us 1 H ^ onepainiflMii Tf H 4-

(B TOM HHcne caMH i H o; ) , ynoB.neTBopHer xora 6bi OAHOM/ aa

ycnoBHii:

(1) ^ HHrae He npHHHMaer aHaneHHa o H f (3?) -f- a,, x: •>>-$,:/?rne ctf H Of - neKOxopbie KOHcxaHTbi.

1 2 ) jf, '(zc) £ a., \Gc 4- ̂ /^ , rne ov H ^f - HeKOTOpwe

i , OHesHflHo, ynosneTBopaeT (1 ) ; a yaoBJierBOpaeT (2) (

KaK &(jc) -^*2Vx ); paaSopo.M cnyiaea HerpynHO nposepHTb, >ITO ecnH

xa>Kflasi Ha (jjyHicuHH G' , /z. yaoBnexBopaer ( 1 ) «nn (2) H ^£=C' <* /4.

£= c/->t- /z. , TO if ynoB.ieTBOpHST ( 1 ) HUH (2) .HHH ,(f

B

3. XII. 1967 r.

/ i H x e p a x y p a

1. P./l.TyacxeflH. MaxeMai/inecKaa nornKa. H/I, 1960.

2. A.H.Manfauea. A.TropuxMbi H peicypCHBHfare 4>yHKUHn. M., 'Ha'yKa"

1965.

80 B.B.KO3bMHHMX

3. Hryen Xwy Hrw.

4. E.A.rlonaKOB.

5. E.A.rlonaKOB.

6. B.A.ycneHCKHft.

OueHKH ana nocnenoBaxenbKocTeft cocroHHHft Ma -

UIHH TbropHHra. FlpoSneMbi Kn6epHeTHKH, 17 (1986),

67-89.

Artre6pbi peKypcHBHbix (j>yKKUHft. AnreSpa n norHKa.

CeMHHap, 3, (1964), 41-56.

O HeKOTopbix cBoflcTBax anreSp peKypcHsnux 4>yHK-

UHft. Anre6pa H norHKa. CeMHHap, 3, N° 3 (1964),

38-57.

JleKUHH O BblHHCJIHMHX ^yHKUHSX. M., 4>H3MaTrH3,

1960.