Abstract
Let T 1 ⊂ T 2 ⊂ ... be arbitrary sets and T = ⋃ ∞ i=1 T i . The space ℓ∞ (T 1, T 2,,...) is defined as the set of all functions z: T ↦ ℝ that are uniformly bounded on every T i (but not necessarily on T). This is a complete metric space with respect to the metric
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
van der Vaart, A.W., Wellner, J.A. (1996). Spaces of Locally Bounded Functions. In: Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2545-2_6
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2545-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2547-6
Online ISBN: 978-1-4757-2545-2
eBook Packages: Springer Book Archive