$B9)A!Bg$NDMK\$G$9(B.

In article <kpisrq$jgj$1@dont-email.me>
"Kyoko Yoshida" <kyokoyoshida123@gmail.com> writes:
> http://www.geocities.jp/a_k_i_k_o928346/def_meromorphic__08.jpg
> $B$3$l$GBg>fIW$+$H;W$$$^$9!#(B

 Corr(A, C^n) $B$H=q$$$F$"$k$N$G$7$g$&$+(B.
 Corr $B$b0UL#ITL@$G$9$7(B, C^n $B$b0UL#ITL@$G$9(B.
 max $B$r$I$&l9g$bGS=|$5$l$k$H$$$&$3$H$r=R$Y$F$$$k(B
$B$D$b$j$+$bCN$l$^$;$s$,(B, $BITL@3N$JDj5A$G$"$k$H$7$+(B
$BI>2A$G$-$^$;$s(B.

> In article <130419172433.M0100475@ras1.kit.ac.jp>
> Tsukamoto Chiaki <chiaki@kit.ac.jp> writes:
> > S $B$r(B D $B$N8IN)E@$+$i$J$k=89g$H$7$F(B,

$B$3$l$O(B, S $B$O(B D $B$NItJ,=89g$G$"$j(B, S $B$N3FE@$O(B S $B$N8IN)E@$G$"$k(B,
$B$H$$$&$3$H$r=R$Y$F$$$^$9(B.

> $B$D$^$j(B,S$B$N85$OK\EZ$+$iN%$l$?>.Eg$N$h$&$J$b$N$G$9$M!#(B

$B!VK\EZ!W$J$s$F9M$($F$$$^$;$s(B.

> $B$=$N:](B,S$B$NE@$r(Ba$B$H$9$k$H(Bz=a$B$,6K$+2D=|FC0[E@$J$i(B
> lim_{z$B"*(Ba}|f(z)|$B$N6K8B$,B8:_$7$^$9$h$M(B($B6K$J$i!g(B,$B2D=|FC0[E@$J$i.Eg(B($B8IN)E@(B)$B$J$N$G(B
> f$B$O(BBall(a,$B&E(B)$B$K$FDj5A$5$l$J$$(B0<$B&E$,I,$:B8:_$7$^$9$h$M!#(B

$B$I$&$7$F$=$&$J$j$^$9$+(B.
 S $B$ONN0h(B($BO"7k3+=89g(B) D $B$NItJ,=89g$G$9$+$i(B,
 S $B$NE@(B a $B$N$"$k6aK5(B Ball(a, \epsilon) $B$O(B D $B$NItJ,=89g$G$"$j(B,
 S $B$NE@(B a $B$O(B S $B$N8IN)E@$G$9$+$i(B, \espilon $B$,==J,$K>.$5$1$l$P(B
 Ball(a, \epsilon) $BFb$N(B S $B$NE@$O(B a $B$@$1$K$J$j$^$9(B.
$B=>$C$F(B, \epsilon $B$,==J,$K>.$5$1$l$P(B,
 Ball(a, \epsilon) \setminus { a } $B$O(B D \setminus S $B$NItJ,=89g$G$"$j(B,
 f $B$O$=$N>e$G@5B'$G$9(B. $BL^O@(B, $BDj5A$5$l$F$$$^$9(B.

> ($B"h(Ba$B$O(BD\setminus S $B$N=8@QE@$G$O$J$$$N$G6K8B$NDj5A$,IT2DG=(B)$B!#(B

$B$=$s$J$3$H$O$"$j$^$;$s(B.

> $B=>$C$F(B,z=a$B$O6K$G$b2D=|FC0[E@$G$b$J$/(B
> http://www.geocities.jp/a_k_i_k_o928346/classification_of_singularity__00.jpg
> $B$h$j8IN)??@-FC0[E@$G$7$+$"$j$^$;$s$M!#(B

$B$3$l$b8m$j(B.

> $B=>$C$F>e5-$N!V(BS $B$r(B D $B$N8IN)E@$+$i$J$k=89g$H$7$F(B,$B!W$O(B
> $B!V(B S $B$r(B f $B$N8IN)FC0[E@$+$i$J$k=89g$H$7$F(B,$B!W$N4V0c$$$G$O$J$$$N$G$7$g$&$+(B?

$BJ8>O$r6J2r$9$k$N$,$*9%$-$J$h$&$G$9$+$i(B,
$B=q$-D>$7$F$*$-$^$7$g$&(B.

$BNN0h(B D $B$NItJ,=89g(B S $B$,$"$C$F(B,
 S $B$N3FE@$O(B S $B$N8IN)E@$G$"$j(B,
 f $B$,(B D $B$+$i(B S $B$r=|$$$?$H$3$m$GDj5A$5$l$F$$$F(B, 
 f $B$,(B D $B$+$i(B S $B$r=|$$$?$H$3$m$G@5B'$G$"$j(B, 
 S $B$NE@$O$I$l$b(B f $B$N??@-FC0[E@$G$J$$$H$-(B, 
 f $B$O(B D $B>e$NM-M}7?4X?t$H8F$P$l$^$9(B. 

> > $B8IN)FC0[E@$G$"$k??@-FC0[E@$N;}$D@-.DjM}$O(B, $BJ#AGJ?LLA4BN$G@5B'$J4X?t$K$D$$$F$NOC$G$9$+$i(B,
 A $B$H$$$&Lu$NJ,$+$i$J$$=89g>e$G$N4X?t$NOC$G$O$"$j$^$;$s(B.

> $B$H$3$m$G(B
> http://www.geocities.jp/a_k_i_k_o928346/def_essential_sigularity__00.jpg
> $B??@-FC0[E@$NNc$r8+$D$1$?$N$G$9$,(B,
> $B2<$+$i(B6$B9TL\$G!X(Bz=z_0$B$GM-3&$G$J$$$,!Y$H$$$&$/$@$j$,$"$j$^$9$,(B,
> $B$3$l$O(Blim_{z$B"*(Bz_0}|f(z)|$B$N6K8B$,B8:_$7$J$$$H$$$&0UL#$KB*$($FBg>fIW$G$7$g$&$+(B
> (lim_{z$B"*(Bz_0}|f(z)|=+$B!g$J$i6K$N==J,>r7o$K$J$C$F$7$^$$$^$9$N$G(B)?

$BM-3&$G$J$$(B, $B$H$$$&$N$O(B z_0 $B$N6aK5(B($B$+$i(B z_0 $B$r=|$$$?NN0h(B) U $B$N>e$G(B,
 |f(z)| \leq M $B$H$J$kl9g$bB8:_$7$J$$>l9g$b$"$j$^$9(B.
$B$@$+$i(B, $BM-3&$G$J$$(B, $B$J$i(B, $B6K$N>l9g$b??@-FC0[E@$N>l9g$b$"$j$^$9(B.

> http://www.geocities.jp/a_k_i_k_o928346/lebesgue_theorem__00.pdf

$BNN0h(B I $B$N!VO$r8+$k$H5$J,$,0-$/$J$k$N$G(B,
$B$b$&8+$^$;$s(B. $B0x$_$K(B,

> $B@~>e$NJ#AG?tCM4X?t(B

$B$rI=$7$?$1$l$P(B, $BFHN)JQ?t$,ZL@$G$-$^$7$?$,$3$l$GBg>fIW$G$7$g$&$+(B?

$B$I$s$J(B \delta $B$KBP$7$F$b(B, $B$H$$$&$3$H$+$i(B, \delta = 1/k $B$H$7$F$b(B,
$B$H8@$($k$o$1$G(B, \delta \geq 1/k $BEy$N=q$-J}$O4V0c$C$F$$$^$9(B.
 Ball((s_0, 1/(k+n)) \setminus { s_0 }) $B$H$$$&5-9fNs$O0UL#$r0Y$5$J$$(B.
 Ball(s_0, 1/(k+n)) \setminus { s_0 } $B$N$3$H$@$H$7$F(B,
 (Ball(s_0, 1/(k+n)) \setminus { s_0 }) \cap A $B$OZL@$K$J$j$^$;$s(B.

> $B$O$$!#(B $BH]Dj$O(B
> http://www.geocities.jp/a_k_i_k_o928346/negation__00.pdf
> $B$H$$$&6q9g$K$J$j$^$7$?$,$3$l$GBg>fIW$G$7$g$&$+(B?

 \lim_{s \to s_0} f(s, x) $B$,B8:_$9$k>l9g$P$+$j$r07$C$F$$$k(B
$B$o$1$G$O$J$$$+$i(B, $B$=$l$r(B \ell $B$KCV$-49$($F5DO@$7$J$$$H(B,
$B2?$r8@$C$F$$$k$N$+J,$+$i$J$$J8>O$K$J$k(B, $B$3$H$O4{$KCm0U$7$^$7$?(B.

> > $B!V6u=89g!W$H!V86E@!W$H$O0c$$$^$9$h(B.
> 
> $B$($C(B? $BJ#AGJ?LL$N86E@$O(B0+0i$B$N;v$@$+$i(B,
> 0+0i=0=$B&U$H$$$&Iw$K6u=89g$K$O$J$i$J$$$N$G$7$g$&$+(B?

$B$J$j$^$;$s(B. $B6u=89g$H(B 0 $B$H$rF10l;k$9$k$N$O(B
$B=89gO@$NCf$G<+A3?t$r9=@.$9$k$H$-$@$1$G$9(B.
$B<+A3?t$KBP1~$9$kJ#AG?t$OB8:_$7$^$9$,(B,
 0 $B$KBP1~$9$kJ#AG?t$=$l<+BN$O6u=89g$G$O$"$j$^$;$s(B.

> lim_{s$B"*(Bs_0}f(s,x)$B$,Hs<}B+$G$"$k;v$r(B
> lim_{s$B"*(Bs_0}f(s,x)=$B!g$HI=5-$9$k$HDj5A$9$l$P(B

$B$@$+$i(B, $B$=$&$$$&Dj5A$OC/$b$7$^$;$s(B.
 lim_{s \to s_0} f(s, x) $B$,<}B+$7$J$$$3$H$H(B,
 lim_{s \to s_0} f(s, x) $B$,%j!<%^%s5eLL$NL58B1sE@$K<}B+$9$k$3$H(B
$B$H$OA4$/0c$C$?35G0$G$9(B.

> $B$I$&$7$F(B,$B?6F0$d%+%*%9$N>uBV$OM-$jF@$J$$$HJ]>Z$G$-$k$N$G$7$g$&$+(B?

$BC1$K!V<}B+$7$J$$!W>l9g$G$"$k$H9M$($F$$$k$@$1$G$9(B.

> $B$9$_$^$;$s!#AjJQ$o$i$:(B
> $Bc>(B $B>$G$OJ#AG?$(D??$Bs$K$b?6F0$9$k%1!<%9$(B❹$B"$k;(B槪ⅸ$BR$Y$i$l$F$k$N$(B\xC7
>  $B%+%*%9$NOC$r$9$k>l9g$K$O$=$&$$$&6hJL$,I,MW$J$3$H$b$"$k$G$7$g$&(B.
>  $B!V$I$&$$$&6hJL$,I,MW$+!W$O!V$I$&$$$&OC$r$9$k$H$-$+!W$K(B $B0MB8$7$^$9(B.$B!Y(B
> $B$N2U=j$,o$NJ#AG?t$K<}B+$7$J$$>l9g$r(B,
$BL58B1sE@$K<}B+$9$k>l9g$H$=$l0J30$KJ,N`$7$?$o$1$G$9$,(B,
$B!V$=$l0J30!W$N=j$r$5$i$K:Y$+$/J,N`$7$F(B,
$BJ,N`$5$l$?$b$N$rJL07$$$9$k$3$H$O$"$k(B,
$B$H$$$&$@$1$G$9(B.

> $B$9$k$H(B,(i)$B$NBP6v$O(B
> lim_{s$B"*(Bs_0}f(s,x)$B":(B{$B!g(B,$B?6F0(B,$B%+%*%9(B} $B"N(B lim_{n$B"*!g(B}f(a_n,x)$B":(B{$B!g(B,$B?6F0(B,$B%+%*%9(B} 
>  for$B"O(B(a_n)$B":(BS
> $B$H$J$C$F$7$^$&$N$G$O$J$$$N$G$7$g$&$+(B?

 \lim_{s \to s_0} f(s, x) is not convergent \Leftrightarrow
 \lim_{n \to infty} f(a_n, x) is not convergent
 for some sequence { a_n } \in S.
$B!V<}B+$7$J$$!W$GLdBj$"$j$^$;$s(B.
 
> "$B6K8B(Blim_{s$B"*(Bs_0}f(s,x)$B$,B8:_$7$J$$(B"$B$H$O(B
> "lim_{s$B"*(Bs_0}f(s,x)$B$,?6F0$9$k$+(B,$B%+%*%9$H$J$k(B"$B$H2rl9g$rK:$l$F$$$^$9(B.

> ($B7+$jJV$7$G$9$,(B)
> $B$G$b(B,$B4v$i%+%*%9$d?6F0$,LGB?$KEP>l$7$J$$$+$i$H8@$C$F(B,
> $BJ#AG4X?t$N6K8B$,J#AG?t$+L58B1sE@$7$+M-$jF@$J$$$H$$$&N)>l$O(B
> $BO@M}E*$K$+$J$jMpK=$J5$$,$7$^$9$,(B
> ($BSH$(LGB?$G$b%+%*%9$d?6F0$H$$$&%1!<%9$,B8:_$9$k8B$j(B,
> limf(z)$B":(BC$B$NH]Dj$O(Blimf(z)=$B!g$N$_$H8@$$J|$C$F$$$$$b$N$G$7$g$&$+(B?)$B!#(B

$B$=$s$J4V0c$C$?$3$H$r8@$C$F$$$k$N$O5.J}$@$1$G$9(B.

> > $BJPHyJ,$r2!$5$($k2D@QJ,4X?t$r;}$A=P$5$J$$(B,
> > $B=iEyE*$JOC$r$9$k$N$G$"$l$P(B,
> >  A $B$r(B R $B$NM-3&JD=89g(B ($BJD6h4V$GNI$$$N$G$O$J$$$G$9$+(B)
> >  B $B$r(B C $B$NNN0h(B
> > $B!!(Bf $B$r(B A \times B $B>e$NO"B3$JJ#AG?tCM4X?t(B
> >  $B3F(B x \in A $B$KBP$7$F(B f(x, s) $B$O(B s $B$K$D$$$FHyJ,2DG=(B
> >  { \partial f \over \partial s }(x, s) = f_s(x, s)
> >  $B$O(B A \times B $B>e$NO"B34X?t(B
> >  $B$H$9$k$H$-(B, F(s) = \int_A f(x, s) dx $B$O(B s $B$N@5B'4X?t$G(B,
> >  F'(s) = \int_A f_s(x, s) dx $B$,@.N)$9$k(B.
> > $B$H$$$&7A$NDjM}$r9M$($k$H$3$m$G$9(B.
> 
> http://www.geocities.jp/a_k_i_k_o928346/prop192_10007__12.jpg
> $B$N(B(iii)$B$G$9$h$M!#(B

$B5.J}$N=q$$$?$b$N$G$O(B f_s(x, s) $B$,O"B34X?t$G$"$k(B, $B$H$$$&>r7o$,(B
$BH4$1$F$$$^$9(B.

> > $B$=$N>ZL@$K$O(B, $B@h$:(B,
> >  A $B$r(B R $B$NM-3&JD=89g(B ($BJD6h4V$GNI$$$N$G$O$J$$$G$9$+(B)
> >  B $B$r(B R $B$NNN0h(B
> > $B!!(Bf $B$r(B A \times B $B>e$NO"B3$Je$NO"B34X?t(B
> >  $B$H$9$k$H$-(B, F(s) = \int_A f(x, s) dx $B$O(B s $B$N(B C^1 $B5i4X?t$G(B,
> >  F'(s) = \int_A f_s(x, s) dx $B$,@.N)$9$k(B.
> 
> http://www.geocities.jp/a_k_i_k_o928346/prop192_100063__03.jpg
> http://www.geocities.jp/a_k_i_k_o928346/prop192_100069__00.jpg
> http://www.geocities.jp/a_k_i_k_o928346/prop192_100069__01.jpg
> $B$He$G=R$Y$?(B,
 
> > $BJPHyJ,$r2!$5$($k2D@QJ,4X?t$r;}$A=P$5$J$$(B,
> > $B=iEyE*$JOC$r$9$k$N$G$"$l$P(B,

$B$H$O4X78$N$J$$OC$,=q$+$l$F$$$k$h$&$G$9$M(B.
$B4X78$,$J$$OC$OFI$_$^$;$s(B.

> > $B$r>ZL@$7$^$9(B. $B2<$,>ZL@$5$l$F$$$l$P(B,
> > $BJ#AGJQ?t(B s $B$NJ#AG?tCM4X?t(B f $B$K$D$$$F$O(B
> > s = u + i v, f = g + i h, F = G + i H $B$H$7$F(B,
> > G, H $B$N(B u, v $BJPHyJ,$K$D$$$F2<$rE,MQ$7(B,
> > G, H $B$N(B u, v $B$K$D$$$F$NJPHyJ,$,O"B3$G$"$j(B,
> > g, h $B$,(B Cauchy-Riemann $B$N4X78<0$rK~$?$9$3$H$+$i(B
> > G, H $B$b(B Cauchy-Riemann $B$N4X78<0$rK~$?$9$3$H$,J,$+$C$F(B,
> > F $B$,@5B'$G$"$k$3$H$,F3$+$l$^$9(B.
> 
> $BBj0U$O(B
> http://www.geocities.jp/a_k_i_k_o928346/prop192_1000695__00.jpg
> $B$G@5$7$$$G$7$g$&$+(B?

$BA4A30c$$$^$9(B.

> http://www.geocities.jp/a_k_i_k_o928346/prop192_10007__13.pdf
> $B$H$J$C$?$N$G$9$,B,EY6u4V(B(A,Brl(A),$B&L(B_R)$B$H(B(B,Brl(B),$B&L(B_C)$B$,(B
> $B&R(Bfinite$B$G$"$k;v$O$I$&$9$l$PJ,$+$j$^$9$G$7$g$&$+(B?

 R, C $B$O(B \sigma-finite $B$G$"$k$3$H$rCN$C$F$$$^$9$+(B.
$B$=$N(B($B%\%l%k(B)$BItJ,=89g$KB,EY$r@)8B$7$?$b$N$b(B
 \simga-finite $B$G$"$k$3$H$,J,$+$j$^$;$s$+(B.
$B$I$&$7$F!V@)8B!W$H$7$F9M$($?$$$N$+$bJ,$+$j$^$;$s$,(B.

> $B$H$$$&;v$O(B
> http://www.geocities.jp/a_k_i_k_o928346/prop192_10007__14.jpg
> $B$G$$$$$N$G$9$M!#(B

$B2?$,NI$$$N$+J,$+$j$^$;$s(B.

> $B$3$l$O(Bf(s)=Re(s)+iIm(s)$B$H$$$&0UL#$G$9$h$M!#(B

 f(s) = (Re f)(s) + i (Im f)(s) $B$H=q$-$?$+$C$?$N$G$7$g$&$+(B.

> http://www.geocities.jp/a_k_i_k_o928346/def_complex_plane_integral__02.jpg
> $B$G$$$$$N$G$9$M!#BgJQM-Fq$&$4$6$$$^$9!#(Bm(_ _)m

$B$O$$(B.
-- 
$BDMK\@i=)(B@$B?tM}!&<+A3ItLg(B.$B4pHW2J3X7O(B.$B5~ET9)7]A!0]Bg3X(B
Tsukamoto, C. : chiaki@kit.ac.jp