POLYNOMIAL APPROXIMATION ON UNBOUNDED SUBSETS AND THE MARKOV MOMENT PROBLEM  2 L  1 L ,Rx        .,exp ! exp ! ... !1 1exp 0            mdttt m x m xx x m xm  xexp Rx  ,Cz   k,0           .0, !12!2!2!1 1exp ,0, !2!2!1 1exp 12122222 2222              t k t k ttt t t k ttt t kkkk kk           ,,0,exp  ktkttk   .; kk       ,0,   tttpp lll  lplim ),0[ K  ,),0[ 1 L  ).,0[   R),0[:     Rtt lim  llh kk ,       ll hlttth lim,,0, ).,0[      lllll plhpp ~ lim,, ~ , ~ ).,0[    .0,,exp  tntn n RA   ,A    ,0  AC  mmp ,A   mm pp ,  . 1 AL   A A m ddp ,lim  P   AL 1  P  . 1 AL     .2,1,0,,,, 2 2121,  ltkjttttx l kj kj R       ,2,1,0, 2 2, 2 1,  lttpttptp llllllll H 21 , AA ,H   .2,1, jA j   21 , AAYY      .; ,2,1,; 11 1 YTTUUTYUY jTATAHTY jj   X ,),0[: 2 Rx  ,),0[ 2   kjx ,     .0,, 2121,  j kj kj tttttx      ., 121 KCXAAK       .2,, YB Zkjkj     YXLF ,1                        ;1,, ,,0,, 121 21 21 ,121 21 21 2 ,,         FXdEdEttF XxdEdEttxxFZkjBxF AA AA AA AA kjkj      ZJJ 21 ,     ,, 21 JkkJj j           .0 ,0 ,0 ,0 1 2 1 1 ,,, 1,1 ,,, 1 21 ,,, 1, ,,, 2 1 1 ,,, ,1 ,,, 21 ,,, , ,,, 2121 2121 2121 2121                         lkji lkji JlkJji lkjilkji JlkJji lkji lkji JlkJji lkjilkji JlkJji lkji lkji JlkJji lkjilkji JlkJji lkji lkji JlkJji lkjilkji JlkJji AAB AAB AAB AAB     x    .21 AA   x       .),0[),0[   cc CC        .,, 212211 AAbaba     2,1,, jba jj 2,1,0,21  jxxx j ,, 21 tt ,2,1,,,,0 ,,   jmxpZmxp jjmjjm ),,0[        .,2,1,2 , 2 ,,   Zmjtrttqtp jjmjjjmjjm 21 P            ., 2 ,, , , , ,            ZkjBxfBxf kjkj kj kjkj kj kjkj  .21 PP               .2,1,,0 21 21 221121     jtRpdEdEtptpppf jjAA AA      211 AACX   YXF 1: .f                   .,, lim limlim ,121 21 21 21 21 1 ,2,,1, 1 ,2,,1, 1 ,2,,1,                                              XxdEdEttx dEdEpp ppfppFxF AA AA AA AA mk j jmjmm mk j jmjmm mk j jmjmm                 .1, , 1 21 21 21       FXF dEdEttFFFX AA AA    )()( ab  □ V V p .V X Y 0 u XS  XA  V    AVS  A S A    YSLf Jj j ,   ,0\~   Yy    YXLF Jj j ,  jSj fF | ., ~ | JjyF Aj  V       , ~ ..0,|..0 ,,, 011 00 uytsptsR AVSuuSVf AV j           .,,1 01 JjXxuxpxF Vj   ., JjF j  HX   ,1 1    n j jzD  ,0,...,0 .D X     1,,,..., 1 1 1 11     n k k n kk nj n j nj jjjjzzzz  nkA k ,...,1,  ,H .,...,1,1 nkA k      .;,,...,1,; 111 YUUVVUYVYnkUAUAHUY kk  Y   .,...,1,1, 1 nkBYB k n kk     1,   jU n j j ,Y   .1,,...,, 1 1 1 1 1  jjjjBBAAU n n nj n j nj n j j       .1,10,...,0,, ~ n jjn j j jXYB      YXBF ,               .,1/1/: ,1/1/ ~ 2 ,, ~ ,1, 11 0 0 1 11 XIBAu uBABF jBFjUF n k k n k k n k k n k k n jjj                                                                                   .;,1,; nj n j jcoAjjSpS    0,,0  j          .11,0 10,...,00,...,0 |     AVV mjmj ppABS      ,,1,0 00               Jj jj Jj jj UfsfBSs  s jU          .1,0, 11 000 11 1 1 1 1 1 1 1 1 1 1 00 BSsusfuuI BA IBBAA BBAAs UUsf n k k n k k nj nj n j j nj nj n j j n j n j nj n jnj n j j Jj j Jj jj                                                                                                   . ~ 1/1/ ~~ 0 1 11 uBBABB n k k n k k                                  □ X Y     YyXx Jj j Jj j   ,  YXLFF ,, 21   YXLF ,         ;,21 JjyxFXxxFxFxF jj   JJ 0   , 0 R Jj j       .,, 1122 00 2112  FFyXx Jj jj Jj jj                 YXBF ,         ; ,,,...,,...,0,, 11      F XBBAAFjUF nn n jj   .,...,,0 1 1 1 1 1 n n nj n j nj n j j jjjBBAAU       ba           .,,0 ,...,,...,,0 1 1 1 1 11 nnj n jnj n j njnjjjj jBBAA BBAAFUX                  .0; ,0:,,...,,..., ,0,, 00 111221212 1 1 1 1 0 0 1 0 2              j nn nj n jnj n j n j jj n j j Jj jj Jj jj n mmm n m mm n m m Jj jj JjJ FFFBBAA BBAAUUU m       ,, YXLF        .,,...,,...,0 11  XBBAAF nn  ,X                    . ,,...,,..., ,...,,..., 11 11        FX FBBAA BBAAFFF nn nn □ n R