Miscellaneous research notes

David Fremlin

The following is an unsystematic, incomplete and erratically updated collection of notes I have written, mostly unpublished. For a further series of notes on specific problems see problems.

  • Postscript to "Measure algebras", 16.4.24 (TeX, PDF).
  • Kirszbraun's theorem, 14.9.18 (TeX, PDF, Postscript).
  • Peres' 33 directions, 16.8.18 (TeX, PDF, Postscript).
  • Illanes's ω-resolvability theorem, 16.9.17 (TeX, PDF, Postscript).
  • Singular homology for amateurs, 11.11.16 (TeX, PDF, Postscript).
  • The Lebesgue density theorem in separable metric spaces, 23.9.16 (TeX, PDF, Postscript).
  • Covering with transversals and extensions of Lebesgue measure, 28.6.16 (TeX, PDF, Postscript).
  • (with J.Mala) Symmetry and measurability, 19.3.16 (TeX, PDF, Postscript).
  • Banach limits on ordinals, 24.12.15 (TeX, PDF, Postscript).
  • p=t, following Malliaris-Shelah and Steprans, 12.12.15 (TeX, PDF, Postscript).
  • On Prokhorov spaces, 19.9.15 (TeX, PDF, Postscript).
  • Stochastic Calculus.
  • Flat GOPS, 20.5.14 (TeX, PDF, Postscript).
  • Lectures on stochastic calculus, 30.10.12 (TeX, PDF, Postscript).
  • The Cascales-Kadets-Rodriguez selection theorem, 27.9.12 (TeX, PDF, Postscript.)
  • Products of gauge integrals, 27.7.11 (TeX (with diagram), PDF, Postscript).
  • Vector-valued gauge integrals, 12.7.11 (TeX, PDF, Postscript).
  • Topological spaces after forcing, 16.6.11 (TeX, PDF, Postscript, abridged PDF version).
  • Measurability in C(2κ) and Kunen cardinals, 31.3.11 (TeX, PDF, Postscript).
  • Well-distributed sequences and Banach density, 28.3.11 (TeX, PDF, Postscript.)
  • Maharam types of amoeba algebras, 31.1.11 (TeX, PDF, Postscript.)
  • Distributive lattices and modular functions, 13.11.10 (TeX, PDF, Postscript.)
  • Vector-valued Saks-Henstock indefinite integrals, 2.9.10 (TeX, PDF, Postscript.)
  • Measure-centering ultrafilters, 7.6.10 (TeX, PDF, Postscript.)
  • Baker's product measures, 19.3.10 (TeX, PDF, Postscript.)
  • Linked sets in probability algebras, 9.12.09 (TeX, PDF, Postscript.)
  • Four problems in measure theory, 29.11.09 (TeX, PDF, Postscript.)
  • On results of M.Elekes and G.Gruenhage, 26.11.09 (TeX, PDF, Postscript.)
  • Give a penny, take a penny, 16.10.09 (TeX, PDF, Postscript.)
  • Nowhere dense filters, 2.9.09 (TeX, PDF, Postscript.)
  • Dependently selective filters, 5.2.09 (TeX, PDF, Postscript.)
  • Invertive extensions, 30.12.08 (TeX, PDF, Postscript.)
  • Ergodic averages, following Austin, 26.11.08 (TeX, PDF, Postscript.)
  • Fair rents, 10.11.08 (TeX, PDF, Postscript.)
  • The density algebra, 6.9.08 (TeX, PDF, Postscript.)
  • Talagrand's example, 3.8.08 (TeX, Postscript).
  • Linking filters, 23.7.08 (TeX, Postscript).
  • Notes on first-return integration, 10.11.07 (TeX, Postscript).
  • Splitting additive functionals, 9.10.07 (TeX, Postscript).
  • Maharam algebras, (TeX, PDF, Postscript).
  • Filters of countable type, 25.9.07 (TeX, Postscript).
  • The McShane and Birkhoff integrals of vector-valued functions, 18.5.07. (TeX, Postscript).
  • m, p and t, following Shelah 885, 24.4.07 (TeX, Postscript).
  • Sums of measures, 11.12.06 (TeX, Postscript).
  • Tube outer measure, 3.12.06 (TeX, Postscript).
  • Alternating functionals, 15.11.06 (TeX, Postscript).
  • Tao's proof of Szemeredi's theorem, 29.9.06 (TeX, Postscript).
  • Tao's removal lemma, 14.7.06 (TeX, Postscript).
  • Random hypergraphs, 27.6.06 (TeX, Postscript).
  • Random equivalence relations, 6.5.06 (TeX, Postscript).
  • Squares in locally compact groups, 1.12.05 (TeX, Postscript.)
  • Hausdorff measures, 30.11.05 (TeX, Postscript).
  • Extension-measurable families of sets, 6.11.05 (TeX, Postscript.)
  • (with M.R.Burke) Cardinal functions of density topologies, 21.9.05 [under construction] (TeX, Postscript.)
  • Baire s-algebras in product spaces, 6.9.05 (TeX, Postscript.)
  • A protocol for machine-based voting, 29.7.05 (TeX, Postscript.)
  • On the zeroes of p and p', 29.7.05 (TeX, Postscript.)
  • Strictly localizable Borel measures, 7.5.05 (TeX, Postscript.)
  • (with D.Preiss) On a problem of W.Ricker, 20.4.05 (TeX, Postscript).
  • Homogeneous measure spaces, 13.4.05 (TeX, Postscript).
  • Extensions of Talagrand's measure, 8.3.05 (TeX, Postscript).
  • A strictly positive Borel measure, 7.3.05 (TeX, Postscript).
  • Lipschitz quotient maps, 9.2.05.
  • On a construction of Gitik & Shelah, 16.1.05.
  • Compact sets without convergent sequences in random real models (with A.Dow), 18.10.04.
  • Dependent multiple choice and Baire's theorem (following Fossy & Morillon), 8.10.04.
  • Postscript to "Consequences of Martin's Axiom", 18.7.04.
  • Poly-linked Boolean algebras, 10.7.04.
  • Partitions of [0,1] into negligible sets (with S.Todorcevic), 26.6.04.
  • Independence-precalibers of measure algebras (with G.Plebanek), 27.4.04.
  • Freese-Nation numbers of finite partially ordered sets (with D.B.Penman), 20.4.04.
  • Radon measures (notes of lectures at Doksy, Czech Rep., Feb. 2004), 21.3.04.
  • Sequences with small difference sets (with M.Laczkovich), 21.3.04.
  • Covering R by translates, 12.2.04.
  • Steffen's Flexihedron, 29.6.03.
  • Freese-Nation numbers, 26.6.03.
  • A singular Borel equivalence relation, 27.4.03.
  • SSP and wQN, 14.1.03.
  • Compact sets of semi-continuous functions, 19.11.02.
  • The generalized Banach contraction theorem, 16.11.02.
  • Notes on Farah's "Analytic Quotients", 16.11.02.
  • Games and the Tukey classification, 4.10.02.
  • On a construction of Steprans, 7.9.02.
  • On a question of Natkaniec, 14.5.01.
  • Supplement to "Real-valued-measurable cardinals", 22.5.00.
  • Invariant measures on metric spaces, 3.5.00.
  • Universally Kuratowski-Ulam spaces, 11.2.00.
  • Supplement to "Weakly alpha-favourable measure spaces", 18.1.00.
  • Postscript to "Saturating ultrafilters on N", 26.7.99 (TeX, PDF, Postscript.)
  • A theorem of Gitik and Shelah on disjoint refinements of sequences of subsets of the real line, 4.4.97.
  • Supplement to `Sequential convergence in Cp(X)', 24.8.92. (TeX, PDF, Postscript.)
  • Notes on the Control Measure Problem (with J.Kupka), 14.5.90.
  • Comparing σ-ideals, 7.5.86.
  • Families of random triples, 16.12.88.
  • Cech-analytic spaces, 10.2.81.

    Referring to these papers

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    4.4.24