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TRANSCRIPT
Am-e5oa n jiornKa, 7, M> 1 (1968), 75-00.
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H M e e r n p s M o f t n e p e c n f i T , H e M a w o p n -
p y e M b l H n p H M H T H B H O p e K y p C H B H O f i 4 > y H K -
u K e H .
flOKASATE/lbCTBO. Hepea \M\M oSoanaHaTb MoniHOCTt, MHO-
KecTBa M
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
'x.(o)=o;
p o
=. ^ j j £ | c e a & t < .r J. I ^ j •{ r I (3-i)f,:\
cjiyiao,
rae oc - MHOMSCTBO H3 /le.MMt! 4.
Ha3OB6M "HHrepBaaoM" MHO/KecrBO Bima
or
ecna
PaCCMOTpMM npOH3BOJlb:ibri5 "
ne nepecexaeTca c HHM, TO
Jl*. ECJIM V!HO>;eCTBO
e, rae Mn«n\tanb-
, HSM HpHMOli H6~
Oo3TOMy npsiMoJi nepecnfeT A/ B
Hblfi 3/ieM6HT /V , ©OJlWJIHft HJ1H
pOClfiT CX B 3TOft TOHK6.
HarypanfcHbift pan pa36HT Ha ciSTHoe HHC.'JO "
3anyM©pyeM "HHrepBanu* ecrec TBeHHbiM oopaaoM (npi inauJOM
^ "HHTepBany*, coaepKameMy <7 : npHnnmeM HOMep
coaep>KaiueMy MUHUMantnoe Hncno, npesbiiuaromee ace nucna 03 "HHrepaa-
na* c HOMepoM jc ).
Ka>Kflbiil "HHTepaan" HMeex PCBHO OHHH HOMep, a Ka:Kaoe HHCJIO eci-fo
HOMep HSKOTOporo 'HHTepeana*.
OnpeaenHM ann ;iio6oro .̂' MHOsiecTBO ^f^Kaic o6i>ennHeKHe scex "HH-
repsanoB*, HOMepa Koxopux HMSIOT BHZI k- 21** ~*~ t ,rae /V^-C1, 0*
nycTb ecTb aononneHHe
"KycKOM* MHOwecrBa /?.'*'' HaaoBeM Ka«<aoe MHOwecrso
me
"icyc-OK*
. HTO
wP. paaeH o6i,enHHeHHio 2L "HHrepsa -
86 B.B.KoabMHHHx
HOB .
Kycoic* MHcmecTBa P-+^ paseH oS-beaHHeHHio HeKoroporo
*KycKa* MHojKecTsa P.'0> H Heicoxoporo "icycKa* MHOJKecxBa P. ( STO
aepHO npH aaxaoM i ).
Oxcioaa cneztyex, HTO nna nK>6oft aenycxoft KOHeinoft cacxeMbi K ,
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
npHMoft nepecnex cc (HMSHHO, B rex XOHKBX, rae 'nepeHHcnawxca*
MS UK , HenocpeflCTB«HHO cnenyioinHe aa He npHHazwtewamHMH UK 'HH -
xepBanaMH* ) .
FIoaroMy npaMofl nepecnfex U/< He MaxcopHpyerca HHnaicoft npHMK -
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
TaK xax anre6pa Po6nHcoHa xoH6HHonopo>KfleHHaa, Kaunas noaa/ireO-
pa BxnroqaeTca B HexoTOpyio MaxcHManbHyro noaanreflpy._ rt fgl
MaxcHManbHaa noaanre6pa, BxnroHaiomaa SM , conep>KHT j- ± , ec-a <.°>nia. i.eM , H He coaepwnr -f ^ , ecnn ceM (HHaqe, Tax xax MBKCH-
^ ^ 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 -
raSpoft).
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
(rax xax cin.tr nepeqacnaror Henepecexaio|iHec9 MHO>KecT-
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 ' •£.
ECHH ^recx . TO fix.) HMeer BHU ^^-t--^ ; emu jcen ,TO
.
EcnH 6bi c: 6una Brepaunefi
UHH <^ , £ 6 bin a 6bi noonpeaeneaiie.M £ ; roraa <x oTflensuiocb 6w
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.