Lp Spaces: Topological Properties

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发表日期：

2025年

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Arup Bose

摘要

In this chapter we make a detailed study of Lp spaces. In particular, for 1 _ p < 1, Lp is a complete normed vector space, and for 0 < p < 1, it is a complete metric space. We shall also give meaning to Lp for p = 1, and learn other interesting properties of these spaces.

In this chapter we make a detailed study of Lp spaces. In particular, for 1 _ p &lt; 1, Lp is a complete normed vector space, and for 0 &lt; p &lt; 1, it is a complete metric space. We shall also give meaning to Lp for p = 1, and learn other interesting properties of these spaces.

Lp Spaces: Topological Properties

摘要

In this chapter we make a detailed study of Lp spaces. In particular, for 1 _ p < 1, Lp is a complete normed vector space, and for 0 < p < 1, it is a complete metric space. We shall also give meaning to Lp for p = 1, and learn other interesting properties of these spaces.