An Arithmetic Property of Riemann Sums

DOI10.2307/2034063zbMath0132.03601OpenAlexW4231785906MaRDI QIDQ5341032

Walter Rudin

Publication date: 1964

Full work available at URL: https://doi.org/10.2307/2034063

zbMATH Keywords

differentiation and integration, measure theory

Related Items (17)

Integration with filters ⋮ A theorem related to Marcinkiewicz-Salem conjecture ⋮ On approximating Lebesgue integrals by Riemann sums ⋮ Approximation of Lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary ⋮ On an example of divergence of Riemann sums ⋮ Almost sure convergence and bounded entropy ⋮ A Pointwise Ergodic Theorem for the Group of Rational Rotations ⋮ On equivalency of martingales and related problems ⋮ On a Riemann Sum Construction of Rudin ⋮ The strong sweeping out property for lacunary sequences, Riemann sums, convolution powers, and related matters ⋮ Some theorems related to almost sure convergence of orthogonal series ⋮ On the sweeping out property for convolution operators of discrete measures ⋮ Sufficient conditions for convergence of Riemann sums for function space defined by the \(k\)-modulus of continuity ⋮ Problems of almost everywhere convergence related to harmonic analysis and number theory ⋮ Convergence of Riemann sums for functions which can be represented by trigonometric series with oefficients forming a monotonic sequence ⋮ Examples and counterexamples for Riemann sums ⋮ Almost sure convergence and square functions of averages of Riemann sums

Cites Work

• On the approximation of Lebesgue integrals by Riemann sums
• On the Behaviour of a Certain Sequence of Functions Derived From a Given One
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