Abstract
In this chapter we (finally...) pick the fruits: We will prove Drinfeld’s Theorem that the Lebesgue measure is the only finitely additive rotationally invariant measure defined on the Lebesgue measurable subsets of the sphere S n for n = 2, 3. (For n ≥ 4, this was proved in Chapter 3, while for n = 1, it is not true! See (2.2.11).) We will also construct, for every prime p, a family of (p + 1)-regular Ramanujan graphs (in particular, giving rise to the best known expanders!).
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© 1994 Springer Basel AG
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Lubotzky, A. (1994). Banach-Ruziewicz Problem for n = 2, 3; Ramanujan Graphs. In: Discrete Groups, Expanding Graphs and Invariant Measures. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0332-4_7
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DOI: https://doi.org/10.1007/978-3-0346-0332-4_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0346-0331-7
Online ISBN: 978-3-0346-0332-4
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