Abstract
Let [a, b] be a closed interval, and E a Banach space. By a step map f: [a, b] → E we mean a map for which there exists a partition P:a = a 0 ≦ a 1 ≦... ≦ a n = b and elements v 1, ...,v n ∈ E such that if a i-1 < t < a i , then f( t) = v i .
Throughout this chapter and the next, we let E, F, G denote Banach spaces.
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© 1993 Springer-Verlag Berlin Heidelberg
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Lang, S. (1993). Differential Calculus. In: Real and Functional Analysis. Graduate Texts in Mathematics, vol 142. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0897-6_13
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DOI: https://doi.org/10.1007/978-1-4612-0897-6_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6938-0
Online ISBN: 978-1-4612-0897-6
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