Let An be a closed set contained in (n, n + 1). Suppose that f: R R

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 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.