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Miklós Schweitzer 1955- Problem 2

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September 30, 2015
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Problem Statement

2. Let f1(x),…,fn(x)f_{1}(x), \dots , f_{n}(x) be Lebesgue integrable functions on [0,1][0,1], with ∫01f1(x)dx=0\int_{0}^{1}f_{1}(x) dx= 0 (i=1,…,n) (i=1,\dots ,n). Show that, for every α∈(0,1)\alpha \in (0,1), there existis a subset EE of [0,1][0,1] with measure α\alpha, such that ∫Efi(x)dx=0\int_{E}f_{i}(x)dx=0. (R. 17)
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