# Shizuo Kakutani

#5,513

Most Influential Person Now

Japanese mathematician

## Shizuo Kakutani's AcademicInfluence.com Rankings

Shizuo Kakutanimathematics Degrees

Mathematics

#308

World Rank

#659

Historical Rank

Measure Theory

#145

World Rank

#227

Historical Rank

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Mathematics

## Shizuo Kakutani's Degrees

- PhD Mathematics Tohoku University

## Why Is Shizuo Kakutani Influential?

(Suggest an Edit or Addition)According to Wikipedia, Shizuo Kakutani was a Japanese-American mathematician, best known for his eponymous fixed-point theorem. Biography Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. At one point he spent two years at the Institute for Advanced Study in Princeton at the invitation of the mathematician Hermann Weyl. While there, he also met John von Neumann.

## Shizuo Kakutani's Published Works

### Published Works

- On Meromorphic Functions. I (1935) (1263)
- A generalization of Brouwer’s fixed point theorem (1941) (1153)
- On Equivalence of Infinite Product Measures (1948) (474)
- Concrete Representation of Abstract (M)-Spaces (A characterization of the Space of Continuous Functions) (1941) (286)
- Concrete Representation of Abstract (L)-Spaces and the Mean Ergodic Theorem (1941) (257)
- Operator-Theoretical Treatment of Markoff's Process and Mean Ergodic Theorem (1941) (175)
- 143. Two-dimensional Brownian Motion and Harmonic Functions (1944) (162)
- Über die Metrisation der topologischen Gruppen (1936) (139)
- Structure and continuity of measurable flows (1942) (137)
- WEAKLY WANDERING SETS AND INVARIANT MEASURES (1964) (132)
- 131. Induced Measure Preserving Transformations (1943) (126)
- Random Ergodic Theorems and Markoff Processes with a Stable Distribution (1951) (107)
- Some characterizations of Euclidean space (1940) (98)
- Two fixed-point theorems concerning bicompact convex sets (1938) (98)
- Nonincrease Everywhere of the Brownian Motion Process (1961) (90)
- A problem of equidistribution on the unit interval [0, 1] (1976) (77)
- Markoff Process and the Dirichlet Problem (1945) (62)
- Invariant measures and orbits of dissipative transformations (1972) (62)
- Invariant measures and orbits of dissipative transformations (1972) (62)
- Invariant measures and orbits of dissipative transformations (1972) (62)
- Infinite measure preserving transformations with “mixing” (1963) (58)
- 56. Topological Properties of the Unit Sphere of a Hilbert Space (1943) (58)
- Über das Haarsche Mass in der lokal bikompakten Gruppe (1944) (58)
- Triple points of Brownian paths in 3-space (1957) (57)
- 131. On Brownian Motions in n-Space (1944) (57)
- Products of symmetries (1958) (55)
- A Proof That there Exists a Circumscribing Cube Around Any Bounded Closed Convex Set in R 3 (1942) (52)
- Strictly ergodic symbolic dynamical systems (1972) (50)
- Birkhoff's Ergodic Theorem and the Maximal Ergodic Theorem (1939) (50)
- Ergodic theory of shift transformations (1967) (47)
- Ring and lattice characterizations of complex Hilbert space (1946) (45)
- The finite topology of a linear space (1963) (41)
- 109. Bohr Compactifications of a Locally Compact Abelian Group II (1943) (41)
- 74. On Cardinal Numbers Related with a Compact Abelian Group (1943) (40)
- 122. Free Topological Groups and Infinite Direct Product Topological Groups (1944) (40)
- On non-denumerable graphs (1943) (40)
- Spectral Analysis of Stationary Gaussian Processes (1961) (38)
- Determination of the spectrum of the flow of brownian motion. (1950) (36)
- 39. Notes on Infinite Product Measure Spaces, II (1943) (34)
- Review: Nobert Wiener, Extrapolation, interpolation, and smoothing of stationary time series with engineering applications (1950) (33)
- A class of multiplicative linear functionals on the measure algebra of a locally compact Abelian group (1960) (32)
- Example of an ergodic measure preserving transformation on an infinite measure space (1970) (30)
- Ein Beweis des Satzes von M. Eidelheit über konvexe Mengen (1937) (29)
- A proof of Beboutov's theorem (1968) (29)
- An example concerning uniform boundedness of spectral measures. (1954) (27)
- Iteration of linear operations in complex Banach spaces (1938) (26)
- 27. Construction of a Non-separable Extension of the Lebesgue Measure Space (1944) (26)
- Weak topology and regularity of Banach spaces (1939) (26)
- Examples of ergodic measure preserving transformations which are weakly mixing but not strongly mixing (1973) (22)
- Simultaneous extension of continuous functions considered as a positive linear operation (1940) (21)
- Concrete Representation of (M)-Spaces (1941) (21)
- Two-dimensional Brownian motion and the type problem of Riemann surfaces (1945) (20)
- I. On the Non-Linear Difference-Differential Equation y1(t) = [A - By(t-r) ly (t) (1958) (19)
- 45. Banach Limits and the Cech Compactification of a Countable Discrete Set (1943) (18)
- On the Uniqueness of Haar's Measure (1938) (18)
- Two Characterizations of Real Hilbert Space (1944) (18)
- Weak Topology, Bicompact Set and the Principle of Duality (1940) (18)
- The decomposition of measures, II (1942) (17)
- Applications of the theory of pseudo-regular functions to the type-problem of Riemann surfaces (1936) (13)
- The speed of convergence in the Ergodic Theorem (1981) (13)
- SOME MULTIPLICATIVE LINEAR FUNCTIONALS ON M(G) (1964) (13)
- Mean Ergodic Theorem in Abstract (L)-Spaces (1939) (13)
- A Proof of Schauder's Theorem (1951) (13)
- Review: Katsumi Nakamura, On a Mode of Definition in Geometry--On Implicit Definition (1941) (12)
- Ergodic theorems and the Markoff process with a stable distribution (1940) (12)
- Full groups and a theorem of dye (1975) (11)
- Markoff process with an enumerable infinite number of possible states (1940) (10)
- Complementing sets of integers - A result from ergodic theory (1992) (9)
- Orbits, sections, and induced transformations (1974) (8)
- RANDOM WALK AND THE TYPE PROBLEM OP RIEMANN SURFACES (1953) (6)
- 73. Normed Ring of a Locally Compact Abelian Group (1943) (5)
- Integral operator with bounded kernel (1938) (5)
- Application of mean ergodic theorem to the problems of Markoff's process (1938) (4)
- Quadratic diameter of a metric space and its application to a problem in analysis (1952) (2)
- Selected papers (1986) (2)
- 18. Notes on Divergent Series and Integrals (1944) (2)
- Representation of Measurable Flows in Euclidean 3-Space. (1942) (2)
- Some Results in the Operator-Theoretical Treatment of the Markoff Process (1939) (2)
- Fixed Point Theorems (1986) (1)
- Development of High Power Column-Type Electric Power Steering System (2007) (1)
- Einführung einer Metrik auf die Riemannsche Fläche und der Typus der Riemannschen Flüche (1937) (1)
- Review: Katsumi Nakamura, On the Concept of Isomorphism in Mathematical Logic (1941) (0)
- REPRESENTA TION OF MEASURABLE FLOWS IN EUCLIDEAN 3-SPA CE (2005) (0)
- Katsumi Nakamura. Sûgakuteki ronrigaku ni okeru “isomorphy” ni tuite (On the concept of isomorphism in mathematical logic). Kagahu-hyooron (The scientific review) , vol. 1 (1936), pp. 11–17. (1941) (0)
- THE OCTOBER MEETING IN NEW YORK The four hundred fiftieth meeting of the American Mathematical (2007) (0)
- On the function m(r, a) in the theory of meromorphic functions (1936) (0)
- Book Reviews: Functional Analysis and Semi-Groups (1949) (0)
- Banach Spaces and Hilbert Spaces (1986) (0)
- On the uniform ergodic theorem concerning real linear operations (1940) (0)
- Hirano Jiro. Kansû, gainen ni tuite (On the concept of a function). Journal of the Mathematical Association of Japan for Secondary Education , vol. 23 (1941), pp. 1–8. (1941) (0)
- LECTURE SERIES IN DIFFERENTIAL EQUATIONS. SESSION II. DYNAMICAL SYSTEMS (1965) (0)
- An Extremum Problem in Product Measure (1942) (0)
- POINTS OF MULTIPLICITY TAU OF PLANE BROWNIAN PATHS (1959) (0)
- Reprint from THE BULLETIN OF THE RESEARCH COUNCIL OF ISRAEL (2004) (0)
- Katsumi Nakamura. Kindai-kikagaku ni yoru hitotu no teigi no sikata (On a mode of definition in geometry—on implicit definition). Kagahu-hyooron (The scientific review) , vol. 2 (1937), pp. 36–41. (1941) (0)
- On she uniform ergodic theorem concerning rent linear operations. (2009) (0)
- On she uniform ergodic theorem concerning rent linear operations. (2009) (0)
- Review: Jiro Hirano, On the Concept of a Function (1941) (0)
- Über ein Metrisationsproblem (1938) (0)
- A Proof of the Uniqueness of Haar's Measure (1948) (0)
- Shizuo Kakutani : Selected Papers (2013) (0)
- REPRESENTA TION OF MEASURABLE FLOWS IN EUCLIDEAN 3-SPA CE (2005) (0)
- On General Quasi-metrie Spaces (1936) (0)

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## What Schools Are Affiliated With Shizuo Kakutani?

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