Sequences and Series of Functions

  • Asuman G. Aksoy
  • Mohamed A. Khamsi
Part of the Problem Books in Mathematics book series (PBM)


• We say that a sequence of functions {f n : D → ℝ} defined on a subset D ⊆ ℝ converges pointwise on D if for each xD the sequence of numbers {f n(x)} converge. If {f n} converges pointwise on D, then we define f : D → ℝ with \(f\left( x \right)\, = \,\mathop {\lim }\limits_{n \to \infty } \,f_n \left( x \right)\) for each xD. We denote this symbolically by f nf on D.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsClaremont McKenna CollegeClaremontUSA
  2. 2.Department of Mathematical SciencesUniversity of Texas at El PasoEl PasoUSA

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