PTITeX 3.4, (c) Personal TeX, Inc. 1985-1998
This is TeX 3.14159 (preloaded format=AMSPLAIN 0.11.30)  28 FEB 2001 13:47
**&AMSPLAIN C:/FPhandbook/henryk-revised-chen.TEX
(C:\FPhandbook\henryk-revised-chen.TEX

AmS-TeX- Version 2.1
COPYRIGHT 1985, 1990, 1991 - AMERICAN MATHEMATICAL SOCIETY
Use of this macro package is not restricted provided
each use is acknowledged upon publication.

(C:\PCTeXv4\AMSTEX\amssym.tex)
! Font \bigbf=p1bx12 scaled 1440 not loadable: Metric (TFM) file not found.
<to be read again> 
                   \relax 
l.1 ...nt\bigbf = p1bx12 scaled \magstep 2
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! Too many }'s.
l.1 ...Hudzik and B. Sims}  Henryk Hudzik}
                                           \vskip 1.5truecm
? 
[1]
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 [2] [3]
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! AmS-TeX error: Invalid use of \\.
\err@ #1->\errmessage {AmS-TeX error: #1}
                                         
l.27 $\Phi (2u) \leq K\Phi (u)\\
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[4]
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 [5] [6] [7]
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 [8]
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 [9]
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 [10]
! Missing $ inserted.
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<to be read again> 
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l.101 
      
? 
! Display math should end with $$.
<to be read again> 
                   \par 
l.101 
      
? 
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \over 
\frac #1#2->{#1\over 
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l.102 \frac{1}{2}
                 \int\limits_{B}[\Phi (x^{\prime \prime }(t)-x_{1}(t)...
? 
! Extra }, or forgotten $.
\frac #1#2->{#1\over #2}
                        
l.102 \frac{1}{2}
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! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.103 
      
? 
[11]
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 [12]
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! Undefined control sequence.
l.134 ... N$ and a subsequence I of ${\cal
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? 
[14]
! Missing $$ inserted.
<to be read again> 
                   (
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? 
! Missing $ inserted.
<inserted text> 
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l.137 
      
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l.137 
      
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<to be read again> 
                   (
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? 
! Missing $ inserted.
<inserted text> 
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<to be read again> 
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l.143 
      
? 
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<to be read again> 
                   \par 
l.143 
      
? 
[15] [16]
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 [23]
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 [24]
! Display math should end with $$.
<to be read again> 
                   .
l.224 ...+\Phi(v))\mu(A)+\Phi(a)\mu(B)=1$.
                                          
? 
[25] [26]
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! AmS-TeX error: Invalid use of \\.
\err@ #1->\errmessage {AmS-TeX error: #1}
                                         
l.231 ...rm (b)} $\Phi\in\Delta_2$ and $\\
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? 
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[27] [28]
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 [29]
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 [30] [31] [32]
Overfull \hbox (7.78748pt too wide) in paragraph at lines 249--249
\teni G[] \ala =$ $\teni G[] \tensy [ \teni G[]$ \ala and $\teni ^^V\ala (\teni
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[33]
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 [34]
Overfull \hbox (23.5606pt too wide) in paragraph at lines 259--260
\ala whenever $\teni I[]\ala (\teni x\ala ) \tensy ^^T \ala 1\teni ; I[]\ala (\
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[35] [36]
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Underfull \hbox (badness 10000) in paragraph at lines 267--267
\tensy 1$ \ala and $\teni I[]\ala (\teni x[]\ala ) \teni < \tensy 1$ \ala for $
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[37] [38]
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 [39]
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 [40]
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 [46]
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Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
 [47] [48] [49]
Underfull \hbox (badness 1178) in paragraph at lines 271--271
\ala One can find by in-duc-tion a se-quence $(\teni n[]\ala )[]$ in $\tenmsb N
$ \ala such that $\teni n[] \ala = 0$, 

\hbox(7.5+3.96402)x367.51447, glue set 2.27635
.\ala O
.\ala n
.\ala e
.\glue 3.33333 plus 1.66666 minus 1.11111
.\ala c
.etc.

[50] [51] [52] [53]
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
 [54] [55]
! Undefined control sequence.
l.271 ...n S(l_\Phi)$ for some $m\in {\cal
                                           N}\}$ holds, where $c_x$ i...
? 
[56]
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
 [57]
Overfull \hbox (23.83806pt too wide) in paragraph at lines 271--271
\ala with $\teni I[] < I[] < [] $\ala , there holds $\teni I[]\ala ((\teni x[] 
\tensy ^^@ \teni x\ala )\teni =d\ala ) = [][] ^^H(\teni x\ala (\teni i\ala )\te
ni =d\ala ) + [][] ^^H(\teni x[]\ala (\teni i\ala )\teni =d\ala ) \tensy ^^T

\hbox(9.8112+4.8334)x367.51447, glue set - 1.0
.\ala w
.\ala i
.\ala t
.\ala h
.\glue 3.33333 plus 1.66666 minus 1.11111
.etc.

[58] [59] [60]
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
 [61]
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no , in font nullfont!
 [62]
Underfull \vbox (badness 6575) has occurred while \output is active
\vbox(509.77824+2.5)x367.51447, glue set 4.03891
.\glue(\topskip) 2.5
.\hbox(7.5+2.5)x367.51447, glue set 0.01935
..\ala R
..\ala e
..\ala c
..\ala a
..\ala l
..etc.
.\penalty 150
.\glue(\baselineskip) 3.88889
.\hbox(6.94444+1.94444)x367.51447, glue set 0.33318
..\teni A
..\mathoff
..\ala .
..\glue 4.44444 plus 4.99997 minus 0.37036
..\ala F
..etc.
.etc.

 [63]
Underfull \vbox (badness 1527) has occurred while \output is active
\vbox(509.77824+4.0)x367.51447, glue set 2.48355
.\glue(\topskip) 2.5
.\hbox(7.5+2.5)x367.51447, glue set 245.47066fil
..\ala f
..\ala u
..\ala n
..\ala c
..\ala t
..etc.
.\penalty 10000
.\glue(\abovedisplayskip) 12.0 plus 3.0 minus 9.0
.\glue(\lineskip) 1.0
.etc.

 [64]
[65]
Missing character: There is no ( in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no ) in font nullfont!
 [66] [67]
Missing character: There is no i in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no . in font nullfont!
 [68] [69] [70] [71] [72] [73] [74] [75] [76] )
(\end occurred inside a group at level 1)
Output written on C:\FPhandbook\henryk-revised-chen.dvi (76 pages, 286556 bytes
).