Конспект лекций по математическому анализу. Шерстнев А.Н. - 359 стр.

  pRIWEDEM DOKAZATELXSTWO DLQ n = 2. pUSTX S = S1  S2 I X; Y 2 S,
TO ESTX
(1)          X = X1  X2; Y = Y1  Y2 (Xk ; Yk 2 Sk ; k = 1; 2):
tOGDA XY = X1 Y1  X2Y2, PRI^EM W SILU (p1) (SM. 191.1) Xk Yk 2 Sk (k =
1; 2), TO ESTX (p1) WYPOLNENO DLQ S. pUSTX W OBOZNA^ENIQH (1) X  Y . |TO
OZNA^AET, W ^ASTNOSTI, ^TO X1  Y1; X2  Y2 I TAK KAK Sk | POLUKOLXCA,
IMEEM
                    X
                    s                         X
                                              t
        Y1 = X1 +          X1j ; Y2 = X2 +          X2j ; Xkm 2 Sk (k = 1; 2):
                    j =1                      i=1

pO\TOMU, Y = (X1 + P X1j )  (X2 + P X2i) = X + P Zj + P Zj0 + P Zji, GDE
                         j             i               j           i     i;j
Zj = X1j  X2 (j = 1; : : :; s); Zj = X1  X2i (i = 1; : : : ; t); Zji = X1j  X2i,
                                  0
^TO OZNA^AET SPRAWEDLIWOSTX (p2) DLQ S: >
    3. z A M E ^ A N I E. eSLI S1 I S2 | KOLXCA MNOVESTW, TO S1  S2 NE
QWLQETSQ, WOOB]E GOWORQ, KOLXCOM (SM. NIVE UPR. 6).
    4. pUSTX mk | MERY (KONE^NO-ADDITIWNYE MERY) NA POLUKOLXCAH
Sk (k = 1; : : : ; n). tOGDA RAWENSTWO
(2)      m(X1  : : :  Xn )  m1X1 
 m2X2 
 : : : 
 mnXn (Xk 2 Sk )
OPREDELQET MERU (SOOTWETSTWENNO KONE^NO-ADDITIWNU@ MERU) m NA Q S .
                                                                                n
                                                                                            k
                                                                                      k=1
  pRIWEDEM DOKAZATELXSTWO DLQ SLU^AQ n = 2. pUSTX
 (3) X = X1  X2 = P X (i); X (i) = X1(i)  X2(i) (i = 1; : : : ; N );
                          i
                                                      Xk(i) 2 Sk (k = 1; 2).
 w SILU 191.8 SU]ESTWU@T KONE^NYE RAZBIENIQ fY1(j)g; fY2(k)g SOOTWET-
STWENNO MNOVESTW X1 I X2 TAKIE, ^TO X1(i) QWLQ@TSQ OB_EDINENIEM NE-
KOTORYH Y1(j), A X2(i) | OB_EDINENIEM NEKOTORYH Y2(k). aDDITIWNOSTX m
SLEDUET IZ RAWENSTW
                            X                         X                       X
 mX = m1X1 
 mX2 =                 m1Y1(j)m2Y2(k) =        m1X1(i)m2X2(i) =       mX (i):
                             j;k                       i                      i

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