Geodesic
Pointwise ergodic theorem for unbounded operators in $\mathbf{L}_2$
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 4, pp. 806-818 Cet article a éte moissonné depuis la source Math-Net.Ru

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A condition implying the strong law of large numbers for trajectories of a normal unbounded operator is given. The condition has been described in terms of a spectral measure. To embrace the case of unbounded operators we pass from the classical arithmetic (Cesàro) means to the Borel methods of summability.
Keywords: strong law of large numbers, individual ergodic theorem, unbounded normal operator, spectral measure, Borel methods of summability, almost sure convergence. 
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R. Jajte. Pointwise ergodic theorem for unbounded operators in $\mathbf{L}_2$. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 4, pp. 806-818. http://geodesic.mathdoc.fr/item/TVP_2005_50_4_a14/

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