Abstract
In this paper, we will investigate the following question: Given C 2 (0,1) and a sequence An [0,1] with (An) = C, when does there exist a subsequence Ani such that (\iAni) > 0? We will show that the answer to this question can be characterized by the properties of a function g which will be a weak L 1 limit of characteristic functions. Before we get started, let’s mention what notation we will be using. L p will denote L p [0,1] with Lebesgue measure , and A will denote the indicator function of A. We will use * to denote weak convergence. All sets will be taken to be Lebesgue measurable. The main result of this paper is given by the following theorem:
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