Abstract
Theorem 6.48 states that a function in \(L^{p^\prime }\) can be regarded as a bounded linear functional on \(L^{p}\). Here we show that a large class of measures can be represented as bounded linear functionals on the space of continuous functions. This is a very important result that has many useful applications and provides a fundamental connection between measure theory and functional analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Ziemer, W.P. (2017). Measures and Linear Functionals. In: Modern Real Analysis. Graduate Texts in Mathematics, vol 278. Springer, Cham. https://doi.org/10.1007/978-3-319-64629-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-64629-9_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64628-2
Online ISBN: 978-3-319-64629-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)