Geodesic
Some Pointwise Convergence Results in Lp (μ), 1 < p < ∞
Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 277-284

Voir la notice de l'article provenant de la source Cambridge University Press

The theory of almost everywhere convergence has its roots in the poineering work of A. Kolmogorov, and today it constitutes one of the most captivating and challenging chapters in modern probability theory and analysis. Whereas some modes of convergence for sequences of measurable functions, e.g. convergence in norm, can be readily obtained by an intelligent exploitation of the various properties of the function spaces involved, a.e. convergence invariably requires a rather high, and sometimes surprising, degree of mathematical virtuosity. 
Duncan, Richard. Some Pointwise Convergence Results in Lp (μ), 1 < p < ∞. Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 277-284. doi: 10.4153/CMB-1977-043-7
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[1] 1. Akcoglu, M. A. and Sucheston, L., Remarks on dilations in Lp-spaces, Proc. Amer. Math. Soc. 53, 80-82 (1975). Google Scholar

[2] 2. Akcoglu, M. A.. A pointwise ergodic theorem in Lp-spaces, Canad. J. Math. 27, 1075-1082 (1975). Google Scholar

[3] 3. Akcoglu, M. A. and Miller, H. D. B., Dominated estimates in Hilbert space, Proc. Amer. Math. Soc, 55, 371-271 (1969). Google Scholar

[4] 4. Burkholder, D. L., Semi-Gaussian subspaces, Trans. Amer. Math. Soc. 104, 123-131 (1962). Google Scholar

[5] 5. Chacon, R. V., A class of linear transformations, Proc. Amer. Math. Soc. 15, 560-564 (1964). Google Scholar

[6] 6. Chacon, R. V., and Olsen, J., Dominated estimates of positive contractions, Proc. Amer. Math. Soc. 20, 266-271 (1969). Google Scholar

[7] 7. de la Torre, A., A simple proof of the maximal ergodic theorem, Can. J. of Math., vol 28, 1073-75 (1976). Google Scholar

[8] 8. Duncan, R. D., Almost everywhere convergence of a class of integrable functions, Z. Wahrscheinliehkeitstheorie verw. Geb. 31, 89-94 (1975). Google Scholar

[9] 9. Duncan, R. D., Pointwise convergence theorems for self-adjoint and unitary contractions, Ann. of Probability vol. 5, No. 4, 622-626 (1977). Google Scholar

[10] 10. Dunford, N., and Schwartz, J., Linear Operators, Vol. I, Wiley-Interscience, New York, 1958. Google Scholar

[11] 11. Garsia, A., Topics in Almost Everywhere Convergence, Chicago, Markham (1970). Google Scholar

[12] 12. Hopf, E., The general temporally discrete Markov process, J. Rat. Mech. Anal. 3, 13-45 (1954). Google Scholar

[13] 13. Ionescu Tulcea, A., Ergodic properties of isometries in Lp spaces, 1 &lt; p &lt; a ∞, Bull. Amer. Math. Soc, 70, 366-371 (1964). Google Scholar

[14] 14. Kaczmarz, S., Sur la convergence et la sommabilité des développements orthogonaux, Studia Math. 1, 87-121 (1929). Google Scholar

[15] 15. Lamperti, J., On the isometries of certain function spaces, Pacific J. Math. 8, 459-466 (1958). Google Scholar

[16] 16. Lessard, S., Th?se de doctorat, l'université de Montréal. Google Scholar

[17] 17. Lorch, E.R., Means of iterated transformations in reflexive vector spaces, Bull. Amer. Math. Soc. 45, 945-947 (1939). Google Scholar

[18] 18. Menshov, D., Sur les séries des fonctions orthogonales, Fundamenta Math. 4, 82-105 (1923). Google Scholar

[19] 19. Riesz, F., Sur la théorie ergodique, Comm. Math. Helv. 17, 221-239 (1945). Google Scholar

[20] 20. Stein, E. M., Topics in harmonie analysis, Annals of Mathematics Studies, no. 63, Princeton University Press (1970). Google Scholar

[21] 21. Yosida, K., Functional Analysis, Springer-Verlag, New York (1966). Google Scholar

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