Abstract
The map \(\mu :{2^{x}} \mathrel\backepsilon B \mapsto \{ _{{\infty otherwise}}^{{card\left( B \right),ifcard\left( B \right) < card\left( {\Bbb N} \right)}} \) is counting measure. If w:X → [0, ∞) is a map, the map μ:2x ∋ B → Σ x ∈ b w(x) is discrete measure. Counting measure and discrete measure are the same iff w = 1. If μ is counting measure on ℕ or ℤ, LP (ℕ, μ) resp. LP(ℤ, μ) are occasionally denoted lP(ℕ) resp. lP(ℤ), 1 ≦ p ≦ ∞.
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© 1982 Springer-Verlag New York Inc.
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Gelbaum, B.R. (1982). L1 (X, μ). In: Problems in Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7679-2_11
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DOI: https://doi.org/10.1007/978-1-4615-7679-2_11
Publisher Name: Springer, New York, NY
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