Theory and principles of electrode processes |
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FourierStieltjes Coefficients FourierStieltjes | 81 |
Convergence and Summability Theorems | 113 |
General Convergence Theorems | 166 |
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absolutely continuous absolutely convergent Borel set bounded variation called characteristic function characteristic function f(t completes the proof constant continuity point continuous function convergence theorem converges almost surely converges to zero converges uniformly converges weakly Corollary defined dF(u dF(x dF{x distribution function F(x equivalent everywhere exists F(oo finite interval Fn(x following theorem Fourier coefficients Fourier series Fourier transform Fourier-Stieltjes transform func function belonging given half-plane Hence holds implies independent random variables inequality inner product space integral inversion formula l)-summable Laplace transform Laplace-Stieltjes transform Lebesgue left-hand side Lemma Let F(x lim sup measurable function necessary and sufficient nondecreasing function nonnegative obvious oo J oo oo oo positive number proof of Theorem Rademacher Rademacher functions radius of convergence right-hand side satisfies Section sequence of independent shows the theorem sin2 summability Suppose sure convergence tion Write X(co Xn(co Zygmund