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An approximate lattice is a discrete approximate subgroup of a locally compact group - i.e. a subset that is closed under multiplication up to an error controlled by a finite set - that has finite co-volume. We study, successively, generalisations of Meyer's theorem in soluble Lie groups, in amenable locally compact groups and in higher-rank semi-simple algebraic groups. 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We study, successively, generalisations of Meyer's theorem in soluble Lie groups, in amenable locally compact groups and in higher-rank semi-simple algebraic groups. Along the way, we investigate properties of closed and discrete approximate subgroups of locally compact groups in general."],"dc:format.checksum.md5":["37931e000dac85cc918d7b75fc85b662"],"dc:identifier.doi":["10.17863/CAM.86438"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/595793c8-df9d-42b2-864a-19f3b6fb1b03/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/339030"],"dc:rights":["https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Mathematics"],"dc:title":["Discrete approximate subgroups of Lie groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"]},"updated_at":"2026-07-22T22:24:28Z"}