MathDB
Miklos Schweitzer 1974_5

Source:

November 12, 2008
functionintegrationreal analysisreal analysis unsolved

Problem Statement

Let {fn}n=0∞ \{f_n \}_{n=0}^{\infty} be a uniformly bounded sequence of real-valued measurable functions defined on [0,1] [0,1] satisfying ∫01fn2=1. \int_0^1 f_n^2=1. Further, let {cn} \{ c_n \} be a sequence of real numbers with ∑n=0∞cn2=+∞. \sum_{n=0}^{\infty} c_n^2= +\infty. Prove that some re-arrangement of the series ∑n=0∞cnfn \sum_{n=0}^{\infty} c_nf_n is divergent on a set of positive measure. J. Komlos
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