State and prove Theorem 28.6 and Corollary 28.8 for an arbitrary compact interval ([a, b]). Data from
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State and prove Theorem 28.6 and Corollary 28.8 for an arbitrary compact interval \([a, b]\).
Data from theorem 28.6
Data from corollary 28.8
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Theorem 28.6 (Weierstra) Polynomials are dense in C[0, 1] w.r.t. uniform convergence. Proof (S. N. Bernstein) Take sequence (Si)ieN of independent2 measur- able functions on ([0, 1], [0, 1], dx) which are Bernoulli (p, 1 - p)-distributed, 0
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Theorem 286 The polynomials are dense in Ca b with respect to uniform convergence ...View the full answer
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