Abstract
Three notions of convergence of sequences of measurable functions, viz. pointwise convergence almost everywhere, almost uniform convergence, and convergence in measure, are introduced and their inter-relationships are examined. It is also shown that each type of convergence is also equivalent to the corresponding Cauchy criterion.
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© 2019 Hindustan Book Agency 2019 and Springer Nature Singapore Pte Ltd.
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Kesavan, S. (2019). Convergence. In: Measure and Integration. Texts and Readings in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-6678-9_4
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DOI: https://doi.org/10.1007/978-981-13-6678-9_4
Publisher Name: Springer, Singapore
Online ISBN: 978-981-13-6678-9
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