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Tm (c ) Tj 1 0 0 1 266.4 354.0 Tm (1+ ) Tj 1 0 0 1 281.3 354.0 Tm (~) Tj 1 0 0 1 81.1 348.5 Tm (n ) Tj 1 0 0 1 226.1 348.5 Tm (n ) Tj 1 0 0 1 257.8 348.5 Tm (n ) Tj 1 0 0 1 310.3 348.5 Tm (\(ii,"on1y ) Tj 1 0 0 1 356.2 348.5 Tm (if"part\) ) Tj 1 0 0 1 397.2 348.5 Tm (Trivially, ) Tj 1 0 0 1 447.6 348.5 Tm (employing ) Tj 1 0 0 1 495.4 348.5 Tm (lemma ) Tj 1 0 0 1 523.2 348.5 Tm (3) Tj 1 0 0 1 53.8 334.8 Tm (as ) Tj 1 0 0 1 67.7 334.8 Tm (n"'~, ) Tj 1 0 0 1 100.3 334.8 Tm (Then ) Tj 1 0 0 1 123.1 334.8 Tm (there ) Tj 1 0 0 1 150.7 334.8 Tm (exists ) Tj 1 0 0 1 184.1 334.8 Tm (a ) Tj 1 0 0 1 194.2 334.8 Tm (constant ) Tj 1 0 0 1 235.0 334.8 Tm (M<~ ) Tj 1 0 0 1 263.0 334.8 Tm (and ) Tj 1 0 0 1 309.4 334.8 Tm (again,) Tj 1 0 0 1 53.8 321.4 Tm (a ) Tj 1 0 0 1 63.4 321.4 Tm (subsequence ) Tj 1 0 0 1 118.6 321.4 Tm ({nO} ) Tj 1 0 0 1 142.1 321.4 Tm (such ) Tj 1 0 0 1 165.4 321.4 Tm (that ) Tj 1 0 0 1 192.5 321.4 Tm (dn'/10g ) Tj 1 0 0 1 229.7 321.4 Tm (cn'~ ) Tj 1 0 0 1 252.7 321.4 Tm (M ) 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Tm (with ) Tj 1 0 0 1 461.5 261.1 Tm (E{Y} ) Tj 1 0 0 1 484.8 261.1 Tm (= ) Tj 1 0 0 1 494.4 261.1 Tm (0 ) Tj 1 0 0 1 503.8 261.1 Tm (and) Tj 1 0 0 1 53.0 247.4 Tm (to ) Tj 1 0 0 1 67.2 247.4 Tm (0 ) Tj 1 0 0 1 76.6 247.4 Tm (as ) Tj 1 0 0 1 90.5 247.4 Tm (n"'~, ) Tj 1 0 0 1 117.6 247.4 Tm (contradicting ) Tj 1 0 0 1 182.6 247.4 Tm (the ) Tj 1 0 0 1 201.6 247.4 Tm (hypothesis. ) Tj 1 0 0 1 266.9 247.4 Tm (QED ) Tj 1 0 0 1 308.9 247.4 Tm (sup ) Tj 1 0 0 1 335.5 247.4 Tm (E{!YI ) Tj 1 0 0 1 363.4 247.4 Tm (t} ) Tj 1 0 0 1 376.6 247.4 Tm (~ ) Tj 1 0 0 1 385.4 247.4 Tm (C, ) Tj 1 0 0 1 406.6 247.4 Tm (Let ) Tj 1 0 0 1 424.3 247.4 Tm (Y1'Y2'" ) Tj 1 0 0 1 461.5 247.4 Tm ('Yn ) Tj 1 0 0 1 480.2 247.4 Tm (be ) Tj 1 0 0 1 493.7 247.4 Tm (iid ) Tj 1 0 0 1 513.1 247.4 Tm (random) Tj 1 0 0 1 53.5 229.0 Tm (Lemma ) Tj 1 0 0 1 79.0 229.0 Tm (4: ) Tj 1 0 0 1 100.6 229.0 Tm (Let ) Tj 1 0 0 1 118.1 229.0 Tm ({a ) Tj 1 0 0 1 132.2 229.0 Tm (} ) Tj 1 0 0 1 141.6 229.0 Tm (,{b} ) Tj 1 0 0 1 173.0 229.0 Tm (and ) Tj 1 0 0 1 192.5 229.0 Tm ({c ) Tj 1 0 0 1 206.6 229.0 Tm (} ) Tj 1 0 0 1 216.0 229.0 Tm (be ) Tj 1 0 0 1 229.0 229.0 Tm (nonnegative ) Tj 1 0 0 1 310.8 229.0 Tm (YEGt,C) Tj 1 0 0 1 52.8 223.9 Tm (---n ) Tj 1 0 0 1 154.6 223.9 Tm (n ) Tj 1 0 0 1 201.1 223.9 Tm (n) Tj 1 0 0 1 53.0 215.3 Tm (number ) Tj 1 0 0 1 85.9 215.3 Tm (sequences, ) Tj 1 0 0 1 307.7 215.3 Tm (variables ) Tj 1 0 0 1 354.7 215.3 Tm (that ) Tj 1 0 0 1 377.0 215.3 Tm (are ) Tj 1 0 0 1 395.5 215.3 Tm (distributed ) Tj 1 0 0 1 451.9 215.3 Tm (as ) Tj 1 0 0 1 464.6 215.3 Tm (Y. ) Tj 1 0 0 1 484.6 215.3 Tm (Then ) Tj 1 0 0 1 508.3 215.3 Tm (for) Tj 1 0 0 1 54.0 201.6 Tm (\(i\) ) Tj 1 0 0 1 77.0 201.6 Tm (If ) Tj 1 0 0 1 90.7 201.6 Tm (r>O, ) Tj 1 0 0 1 117.6 201.6 Tm (then ) Tj 1 0 0 1 308.2 201.6 Tm (each ) Tj 1 0 0 1 330.7 201.6 Tm (E>O ) Tj 1 0 0 1 353.8 201.6 Tm (there ) Tj 1 0 0 1 381.4 201.6 Tm (exists ) Tj 1 0 0 1 414.7 201.6 Tm (a ) Tj 1 0 0 1 424.6 201.6 Tm (constant ) Tj 1 0 0 1 465.4 201.6 Tm (K ) Tj 1 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577.0 Tm (the ) Tj 1 0 0 1 494.2 577.0 Tm (second ) Tj 1 0 0 1 527.3 577.0 Tm (part) Tj 1 0 0 1 67.7 570.7 Tm (~:\(42\) ) Tj 1 0 0 1 119.5 570.7 Tm (is ) Tj 1 0 0 1 132.5 570.7 Tm (obtained ) Tj 1 0 0 1 175.4 570.7 Tm (by ) Tj 1 0 0 1 188.9 570.7 Tm (inspecting ) Tj 1 0 0 1 239.3 570.7 Tm (the ) Tj 1 0 0 1 257.8 570.7 Tm (proof ) Tj 1 0 0 1 285.4 570.7 Tm (of ) Tj 1 0 0 1 318.2 570.7 Tm (of ) Tj 1 0 0 1 331.7 570.7 Tm (the ) Tj 1 0 0 1 350.9 570.7 Tm (theorem, ) Tj 1 0 0 1 392.2 570.7 Tm (we ) Tj 1 0 0 1 406.8 570.7 Tm (remark ) Tj 1 0 0 1 439.0 570.7 Tm (that) Tj /FontHelvetica 6.0 Tf 1 0 0 1 334.1 558.5 Tm (~) Tj /FontHelvetica 8.0 Tf 1 0 0 1 67.4 556.6 Tm ([11 ) Tj 1 0 0 1 83.3 556.6 Tm (,theorem ) Tj 1 0 0 1 124.3 556.6 Tm (1], ) Tj 1 0 0 1 147.4 556.6 Tm (To ) Tj 1 0 0 1 161.5 556.6 Tm (show ) Tj 1 0 0 1 184.1 556.6 Tm (\(44\), ) Tj 1 0 0 1 212.4 556.6 Tm (let ) Tj 1 0 0 1 230.2 556.6 Tm (>0 ) Tj 1 0 0 1 248.4 556.6 Tm (be ) Tj 1 0 0 1 314.2 556.6 Tm (p{ ) Tj 1 0 0 1 333.4 556.6 Tm (U ) Tj 1 0 0 1 349.7 556.6 Tm ({M ) Tj 1 0 0 1 370.3 556.6 Tm (>q ) Tj 1 0 0 1 391.4 556.6 Tm (.+ ) Tj 1 0 0 1 403.7 556.6 Tm (t}} ) Tj 1 0 0 1 428.4 556.6 Tm (~) Tj 1 0 0 1 68.2 542.6 Tm (arbitrary, ) Tj 1 0 0 1 123.8 542.6 Tm (We ) Tj 1 0 0 1 137.5 542.6 Tm (will ) Tj 1 0 0 1 160.3 542.6 Tm (extend ) Tj 1 0 0 1 193.0 542.6 Tm (the ) Tj 1 0 0 1 212.2 542.6 Tm (proof ) Tj 1 0 0 1 239.5 542.6 Tm (of ) Tj 1 0 0 1 253.7 542.6 Tm (a ) Tj 1 0 0 1 262.3 542.6 Tm (theorem ) Tj 1 0 0 1 327.6 542.6 Tm (k=n, ) Tj 1 0 0 1 365.3 542.6 Tm (k ) Tj 1 0 0 1 383.5 542.6 Tm (ffiln ) Tj 1 0 0 1 431.5 542.6 Tm (~) Tj 1 0 0 1 67.2 529.9 Tm (of ) Tj 1 0 0 1 81.8 529.9 Tm ([12]. ) Tj 1 0 0 1 115.2 529.9 Tm (In ) Tj 1 0 0 1 128.6 529.9 Tm (particular, ) Tj 1 0 0 1 183.8 529.9 Tm (we ) Tj 1 0 0 1 198.2 529.9 Tm (show ) Tj 1 0 0 1 221.3 529.9 Tm (that ) Tj 1 0 0 1 245.0 529.9 Tm (\(44\) ) Tj 1 0 0 1 266.9 529.9 Tm (holds ) Tj 1 0 0 1 415.0 529.9 Tm (P{ ) Tj 1 0 0 1 430.8 529.9 Tm (U ) Tj 1 0 0 1 444.2 529.9 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502.3 Tm (note ) Tj 1 0 0 1 225.6 502.3 Tm (that ) Tj 1 0 0 1 248.6 502.3 Tm (by ) Tj 1 0 0 1 396.7 502.3 Tm (+ ) Tj 1 0 0 1 406.8 502.3 Tm (P[ ) Tj 1 0 0 1 421.4 502.3 Tm (U ) Tj 1 0 0 1 433.2 502.3 Tm ({Q\(>: ) Tj 1 0 0 1 470.6 502.3 Tm (q. ) Tj 1 0 0 1 502.3 502.3 Tm (-I-t/'2}}) Tj /FontHelvetica 7.0 Tf 1 0 0 1 156.5 486.7 Tm (.k-1 ) Tj 1 0 0 1 487.7 486.7 Tm (ffiln) Tj /FontHelvetica 8.0 Tf 1 0 0 1 67.0 487.4 Tm (Chebyshev's ) Tj 1 0 0 1 123.8 487.4 Tm (inequal1ty ) Tj 1 0 0 1 173.8 487.4 Tm (and ) Tj 1 0 0 1 193.2 487.4 Tm (by ) Tj 1 0 0 1 207.8 487.4 Tm (\(43\), ) Tj 1 0 0 1 417.6 487.4 Tm (k"-n,) Tj /FontHelvetica 7.0 Tf 1 0 0 1 135.8 480.2 Tm (-1 ) Tj 1 0 0 1 155.3 480.2 Tm (k) Tj /FontHelvetica 14.0 Tf 1 0 0 1 230.6 475.0 Tm (I) Tj /FontHelvetica 6.0 Tf 1 0 0 1 359.0 475.0 Tm (~) Tj /FontHelvetica 8.0 Tf 1 0 0 1 111.6 468.2 Tm (Pfll~ ) Tj 1 0 0 1 147.4 468.2 Tm (.}: ) Tj 1 0 0 1 167.0 468.2 Tm (Y1r~c} ) Tj 1 0 0 1 208.8 468.2 Tm (~e- ) Tj 1 0 0 1 234.7 468.2 Tm (Alck. ) Tj 1 0 0 1 331.9 468.2 Tm (=p[ ) Tj 1 0 0 1 357.8 468.2 Tm (U ) Tj 1 0 0 1 369.8 468.2 Tm ([Q\(Xk-lq ) Tj 1 0 0 1 431.0 468.2 Tm (,+t/2\)\)) Tj 1 0 0 1 151.4 457.2 Tm (1=1, ) Tj 1 0 0 1 352.6 457.2 Tm (k=n, ) Tj 1 0 0 1 393.8 457.2 Tm (.mln) Tj 1 0 0 1 117.4 439.7 Tm (\(E{eAY}\)k+\(E[e-AY}\)k\) ) Tj 1 0 0 1 318.0 439.7 Tm (for ) Tj 1 0 0 1 336.2 439.7 Tm (all ) Tj 1 0 0 1 354.0 439.7 Tm (n ) Tj 1 0 0 1 363.6 439.7 Tm (large ) Tj 1 0 0 1 391.0 439.7 Tm (enough ) Tj 1 0 0 1 424.6 439.7 Tm (in ) Tj 1 0 0 1 438.0 439.7 Tm (view ) Tj 1 0 0 1 461.0 439.7 Tm (of ) Tj 1 0 0 1 475.7 439.7 Tm (\(22\), ) Tj 1 0 0 1 505.7 439.7 Tm (Thus, ) Tj 1 0 0 1 535.4 439.7 Tm (if) Tj 1 0 0 1 61.4 427.0 Tm (~2c-IAlck.'eIA ) Tj 1 0 0 1 140.4 427.0 Tm (!kC/2 ) Tj 1 0 0 1 175.0 427.0 Tm (for ) Tj 1 0 0 1 190.6 427.0 Tm (all ) Tj 1 0 0 1 207.4 427.0 Tm (A~[-c\(t/2\),+c\(t/2\)] ) Tj 1 0 0 1 317.3 427.0 Tm (Qnvqmin+qmin ) Tj 1 0 0 1 382.1 427.0 Tm (WPl ) Tj 1 0 0 1 400.8 427.0 Tm (as ) Tj 1 0 0 1 414.5 427.0 Tm (n+oo, ) 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