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On Equivalence of Infinite Product Measures
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“Accordingly, the generalised angle between arbitrary quantum states is given by the Bures angle [64,65]”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [64]
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Items 401–426 of 426
Approximation of Improper Prior Measures by Prior Probability Measures
Stein, C. (1965) · Springer eBooks · doi:10.1007/978-3-642-49749-0_13
Baker, C. R. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0005.pub2
Kukush, A. (2019) · doi:10.1002/9781119476825.refs
(1972) · Pure and applied mathematics · doi:10.1016/s0079-8169(08)60127-0
Baker, C. R. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat02814
Ergodic Theory: Nonsingular Transformations
Danilenko, A. I., & Silva, C. E. (2022) · Encyclopedia of Complexity and Systems Science · doi:10.1007/978-3-642-27737-5_183-2
Phase transitions for non-singular Bernoulli actions
Berendschot, T. (2023) · Ergodic Theory and Dynamical Systems · doi:10.1017/etds.2023.24
Orthogonality of invariant measures for weighted shiftsPreprint
Grivaux, S., Matheron, É., & Menet, Q. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2312.13920
Orthogonality of measures and states
Mejak, S. (2024) · Fundamenta Mathematicae · doi:10.4064/fm209-9-2023
Extremal invariant distributions of infinite Brownian particle systems with rank dependent drifts
Banerjee, S., & Budhiraja, A. S. (2024) · Probability Theory and Related Fields · doi:10.1007/s00440-024-01305-0
Wang, S., & Yang, T. (2024) · SIAM Journal on Mathematical Analysis · doi:10.1137/23m1562123
Fourteen lectures on inference for stochastic processes
Рао, Б. Л. С. П. (2024) · Handbook of statistics · doi:10.1016/bs.host.2024.07.003
On the Lebesgue measure of one generalised set of subsums of geometric series
Makarchuk, O. P., & Karvatskyi, D. (2024) · Matematychni Studii · doi:10.30970/ms.62.2.115-120
A continuum of invariant measures for the periodic KdV and mKdV equations
Chapouto, A., & Forlano, J. (2025) · Transactions of the American Mathematical Society · doi:10.1090/tran/9489
A geometric quantum speed limit: Theoretical insights and photonic implementation
Wang, Q., Wang, B., Wang, J., & Zhang, L. (2025) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-025-2691-9
Structure of the distribution of one class of generalized Bernoullie convolutions
Makarchuk, O. P., & Khaletsky, B. (2025) · Bulletin of Taras Shevchenko National University of Kyiv Series Physics and Mathematics · doi:10.17721/1812-5409.2025/1.6
Minimum Hellinger distance estimates for a periodic fractional autoregressive model
Benaklef, N., Belaide, K., & Seba, D. (2025) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2025.2566832
A threshold for Poisson behavior of non-stationary product measures
Hochman, M., & Paviato, N. (2025) · Ergodic Theory and Dynamical Systems · doi:10.1017/etds.2025.10258
Challenging Problems in Singular Dynamical Systems
Klauder, J. R. (1976) · Springer eBooks · doi:10.1007/978-3-7091-8473-8_12
Algorithmic randomness and the weak merging of computable probability measures
Huttegger, S. M., Walsh, S., & Blando, F. Z. (2026) · Annals of Pure and Applied Logic · doi:10.1016/j.apal.2026.103737
Chapouto, A., Li, G., & Oh, T. (2026) · Journées Équations aux dérivées partielles · doi:10.5802/jedp.692
Cylindrical Yield-Curve Dynamics and the Arbitrage-Free Class *Preprint
Huang, S., & Cao, Z. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7444240
A Riesz Product Type Measure on the Cantor Group
Shi, Q. (2010) · Communications in Mathematical Research · doi:10.4208/cmr.v26.n1.p7
Cao, Z., & Huang, S. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7637018
Introduction to the Theory of Hypothesis Testing
Schmetterer, L. F. (1974) · Springer eBooks · doi:10.1007/978-3-642-65542-5_5
Metadata
- Authors
- Kakutani, S.
- Corresponding author
- Kakutani, Shizuo
- Venue
- The Annals of Mathematics
- Publisher
- JSTOR
- Published
- 1948-01
- Volume
- 49
- Issue
- 1
- Pages
- 214
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2320259161
- Cited by
- 424
- References
- 0
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 10 · 2023: 8 · 2022: 10 · 2021: 9 · 2020: 12 · 2019: 11 · 2018: 16 · 2017: 7 · 2016: 8 · 2015: 15 · 2014: 11 · 2013: 12 · 2012: 13
- FWCI
- 3.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Annals of Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Mathematics › Mathematical Physics › p-Adic Analysis and Mathematical Physics
- Keywords
- measurement invariance, product probability spaces
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