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Pointwise Blow-up of Sequences Bounded in L1

✍ Scribed by Milton C. Lopes Filho; Helena J. Nussenzveig Lopes

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
263
Category
Article
ISSN
0022-247X

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✦ Synopsis

Given a sequence of functions bounded in L 1 0 1 , is it possible to extract a subsequence that is pointwise bounded almost everywhere? The main objective of this note is to present an example showing that this is not possible in general. We will also prove a pair of positive results. We show that if the sequence of functions consists of multiples of characteristic functions of measurable sets, the answer is yes. We also show that it is always possible to extract a subsequence that is pointwise bounded on a countable, dense set of points.

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