Question: Let An be a closed set contained in (n, n + 1). Suppose that f: R R satisfies Arf = (1)n/n and f = 0

Let An be a closed set contained in (n, n + 1). Suppose that f: R →R satisfies ∫Arf = (−1)n/n and f = 0 outside Un An.. Find two partitions of unity Φ and Ψ such that ∑ǿЄΦ∫Rǿ∙f and ∑ǿЄΦ∫Rψ∙f converge absolutely to different values.

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