Claude Ambrose Rogers
British mathematician
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(Suggest an Edit or Addition)According to Wikipedia, Claude Ambrose Rogers FRS was an English mathematician who worked in analysis and geometry. Research Much of his work concerns the Geometry of Numbers, Hausdorff Measures, Analytic Sets, Geometry and Topology of Banach Spaces, Selection Theorems and Finite-dimensional Convex Geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers lemma and the Dvoretzky–Rogers theorem, both with Aryeh Dvoretzky. He constructed a counterexample to a conjecture related to the Busemann–Petty problem. In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres.
Claude Ambrose Rogers's Published Works
Published Works
- Packing and Covering (1964) (419)
- The difference body of a convex body (1957) (261)
- The realization of distances within sets in Euclidean space (1972) (259)
- The Packing of Equal Spheres (1958) (241)
- Absolute and Unconditional Convergence in Normed Linear Spaces. (1950) (192)
- Covering a sphere with spheres (1963) (146)
- Convex Bodies Associated with a Given Convex Body (1958) (135)
- Borel selectors for upper semi-continuous set-valued maps (1985) (129)
- A note on coverings (1957) (117)
- Functions continuous and singular with respect to a Hausdorff measure (1961) (109)
- The directions of the line segments and of the r -dimensional balls on the boundary of a convex body in Euclidean space (1970) (104)
- On Two-Distance Sets in Euclidean Space (1977) (93)
- Some extremal problems for convex bodies (1958) (92)
- The existence of a centrally symmetric convex body with central sections that are unexpectedly small (1975) (88)
- K-analytic sets (1983) (88)
- The Construction of Certain Graphs (1966) (81)
- Mean values over the space of lattices (1955) (74)
- Covering space with convex bodies (1962) (74)
- The Moment Problem for Unimodal Distributions (1951) (67)
- Existence Theorems in the Geometry of Numbers (1947) (65)
- Representation Theorems for Distribution Functions (1958) (65)
- A Single Integral Inequality (1957) (63)
- The closest packing of convex two-dimensional domains (1951) (61)
- σ-fragmentable Banach spaces (1992) (61)
- Covering space with equal spheres (1959) (59)
- The analysis of additive set functions in Euclidean space (1959) (58)
- Lattice coverings of space (1959) (57)
- The Number of Lattice Points in a Set (1956) (57)
- LECTURES ON DIOPHANTINE APPROXIMATIONS (1964) (50)
- Covering convex bodies by translates of convex bodies (1997) (49)
- Covering the Plane with Convex Sets (1952) (47)
- Hlawka’s theorem in the geometry of numbers (1947) (43)
- The Problem of Subsets of Finite Positive Measure (1969) (41)
- A Note on Coverings and Packings (1950) (40)
- Topological Properties of Banach Spaces (1993) (37)
- Norm fragmented weak* compact sets (1990) (36)
- Continuous Functions on Totally Ordered Spaces That Are Compact in Their Order Topologies (2000) (32)
- A Less Strange Version of Milnor's Proof of Brouwer's Fixed-Point Theorem (1980) (31)
- A convex body with a false centre is an ellipsoid (1971) (28)
- Lattice Coverings of Space: The Minkowski–Hlawka Theorem (1958) (28)
- Fragmentability and σ-fragmentability (1993) (26)
- The product ofn real homogeneous linear forms (1950) (26)
- Symmetrical sets of constant width and their partitions (1971) (26)
- Additive set functions in Euclidean space. II (1963) (25)
- The Compound of Convex Bodies (1957) (24)
- Two Integral Inequalities (1956) (23)
- Siegel's mean value theorem in the geometry of numbers (1958) (22)
- Borel isomorphisms at the first level—I (1979) (21)
- On coverings with convex domains (1964) (21)
- Analytic sets in Hausdorff spaces (1964) (20)
- A locally uniformly convex renorming for certain ℒ(K) (1990) (20)
- Upper semi-continuous set-valued functions (1982) (20)
- REAL FUNCTIONS (Lecture Notes in Mathematics 1170) (1987) (19)
- Increasing Paths on the One‐Skeleton of a Convex Body and the Directions of Line Segments on the Boundary of a Convex Body (1971) (19)
- On the uniformization of sets in topological spaces (1968) (19)
- The moments of the number of points of a lattice in a bounded set (1955) (18)
- Indefinite Quadratic Forms in n Variables (1952) (18)
- Durham Symposium on the Relations between Infinite-Dimensional and Finite-Dimensional Convexity (1976) (16)
- The Collected Works Of Harold Davenport (1977) (16)
- Paths in the one-skeleton of a convex body (1970) (15)
- The covering of n-dimensional space by spheres (1953) (15)
- The star number of coverings of space with convex bodies (1964) (15)
- Some Problems in the Geometry of Convex Bodies (1981) (14)
- Borel selectors for upper semi-continuous multi-valued functions (1984) (13)
- The extremal structure of convex sets (1977) (13)
- An Asymptotic Expansion for Certain Schläfli Functions (1961) (12)
- A Linear Borel set whose Difference set is not a Borel set (1970) (12)
- Continuous Functions on Compact Totally Ordered Spaces (1995) (11)
- The Signatures of the Errors of Simultaneous Diophantine Approximations (1950) (11)
- A modified form of Siegel's mean-value theorem (1955) (11)
- Descriptive Borel sets (1965) (11)
- Some Sets of Continued Fractions (1964) (10)
- Boundaries of and selectors for upper semi-continuous multi-valued maps (1985) (10)
- Piece-wise closed functions (1984) (10)
- The Product of n Homogeneous Linear Forms (1949) (10)
- The Descriptive Character of Certain Universal Sets (1973) (9)
- Diophantine inequalities with an infinity of solutions (1950) (9)
- An intersection property of sets with positive measure (1963) (9)
- Sets non-σ-finite for Hausdorff measures (1962) (9)
- An equichordal problem (1981) (9)
- σ-fragmented Banach spaces II (1994) (9)
- The Finite Dimensional Skeletons of a Compact Convex Set (1973) (8)
- Lattice Coverings of Space with Convex Bodies (1958) (8)
- The Normability of Metrizable Sets (1973) (8)
- The Number of Lattice Points in a Star Body (1951) (8)
- Continuous functions on products of compact Hausdorff spaces (1999) (8)
- THE AMOUNT OF OVERLAPPING IN PARTIAL COVERINGS OF SPACE BY EQUAL SPHERES (1964) (8)
- On the projection of Souslin sets (1966) (7)
- Hausdorff Measure and Local Measure, II (1982) (7)
- Piece-wise closed functions and almost discretely σ-decomposable families (1985) (7)
- Functions of the First Baire Class (1988) (7)
- Theorems of Novikov type (1977) (6)
- A Conjecture of Chowla (1951) (6)
- The Critical Determinant of a Convex Cylinder (1948) (6)
- On Theorems of Siegel and Hlawka (1951) (6)
- The Volume of a Polyhedron Inscribed in a Sphere (1953) (6)
- The convex generation of convex Borel sets in euclidean space (1970) (5)
- Borel isomorphisms at the first level: Corrigenda et addenda (1980) (5)
- Separation of K –analytic sets (1985) (5)
- ON THE CRITICAL DETERMINANTS OF CYLINDERS (1950) (5)
- Partly Convex Peano Curves (1983) (5)
- Probability Measures on Compact Sets (1986) (5)
- A Note on the Geometry of Numbers (1949) (5)
- The Successive Minima of Measurable Sets (1949) (5)
- The Asymptotic Directions of n Linear Forms in n+1 Integral Variables (1950) (5)
- On hausdorff measures in topological spaces (1963) (4)
- Invariance of borel classes in metric spaces (1983) (4)
- Richard Rado, 28 April 1906 - 23 December 1989 (1991) (4)
- Lusin's First Separation Theorem (1971) (4)
- Lusin's Second Separation Theorem (1973) (4)
- RADON MEASURES ON BANACH SPACES WITH THEIR WEAK TOPOLOGIES (1995) (3)
- Erratum to: The closest packing of convex two-dimensional domains,corrigendum (1960) (3)
- The Product of n Non‐Homogeneous Linear Forms (1954) (3)
- Scales of functions (1960) (3)
- Almost periodic critical lattices (1953) (3)
- Dimension prints of fractal sets (1994) (3)
- A Classification of Path-Finite Trees (1973) (2)
- Linear Transformations Which Apply To All Convergent Sequences and Series (1946) (2)
- A Note on the Theorem of Macbeath (1954) (2)
- Dense scales of functions (1961) (2)
- On the Law of the Iterated Logarithm (1962) (2)
- Spaces with Good Borel Structures (1970) (2)
- The Successive Minima of a Convex Cylinder (1949) (2)
- Compact Borelian Sets (1970) (2)
- The Minkowski-Hlawka theorem (1954) (1)
- Uniform set functions (1961) (1)
- Universal Properties of Certain Analytic Sets (1977) (1)
- The Topological Classification of Open Co-Countable Subsets of S2 (1978) (1)
- UNSOLVED AND UNSOLVABLE PROBLEMS IN GEOMETRY (1967) (1)
- The reduction of star sets (1952) (1)
- A modified form of Siegel's mean value theorem. II (1958) (1)
- Piece-wise closed functions: Corrigendum (1984) (1)
- The Potency of Polish Spaces: Retractions: Restrictions (1982) (1)
- Descriptive sets (1966) (1)
- Beta and Gamma distributions (1956) (1)
- The Chance That a Point Should Be Near the Wrong Lattice Point (1962) (1)
- The Transformation of Sequences by Matrices (1950) (1)
- Large discs in convex unions (1988) (1)
- K -analytic sets: corrigenda et addenda (1984) (1)
- ON THE CRITICAL DETERMINANT OF A CERTAIN NON-CONVEX CYLINDER (1949) (1)
- Chapter 5. Applications (2009) (0)
- Chapter 4. Selectors for compact sets (2009) (0)
- Chapter 1. Classical results (2009) (0)
- Proceedings of the meetings for the years 1908, 1909, 1910 / Committee on publication, James E. Rice, Howard C. Pierce, Raymond Pearl ; C.A. Rogers, ed. (0)
- The Geometry of Numbers (2011) (0)
- Chapter 3. Selectors for upper semi-continuous functions with non-empty compact values (2009) (0)
- Chapter 2. Functions that are constant on the sets of a Functions that are constant on the sets of a disjoint discretely σ-decomposable family of Fσ-sets (2009) (0)
- Chapter 7. Further applications (2009) (0)
- EXTREMAL VALUES OF CONTINUANTS (2010) (0)
- Length, area and volume (1973) (0)
- Chapter 6. Selectors for upper semi-continuous set-valued maps with nonempty values that are otherwise arbitrary (2009) (0)
- Spaces Absolute and Unconditional Convergence in Normed Linear (0)
- The Second Separation Theorems (1977) (0)
- Acknowledgement for "A Conjecture of Chowla" (1953) (0)
- LATTICE POINTS (Pitman Monographs 39) (1990) (0)
- Erratum to: Upper semi-continuous set-valued functions (1985) (0)
- SPACE AND SPACES (1969) (0)
- A study of Convex Cones from the point of view of the Geometry of Numbers. (1968) (0)
- Certain Integrals Over Convex Sets (1953) (0)
- A Condition For a Real Lattice to Define a Zeta Function. (1951) (0)
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