Ergodic Theorems for Group Actions - A. A. Tempelman

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Résumé :
1: Means and averageable functions.- 2: Ergodicity and mixing.- 3: Averaging sequences. Universal ergodic theorems.- 4: Mean ergodic theorems.- 5: Maximal and dominated ergodic theorems.- 6: Pointwise ergodic theorems.- 7: Ergodic theorems for homogeneous random measures.- 8: Specific informational and thermodynamical characteristics of homogeneous random fields.- ? 1. Groups and semigroups.- ? 2. Homogeneous and group-type homogeneous spaces.- ? 3. Amenable semigroups and ergodic nets.- ? 4. Positive definite functions.- ? 5. Representations of semigroups in Banach spaces.- ? 6. Weakly almost periodic elements and functions.- ? 7. Dynamical systems.- ? 8. Homogeneous random functions.- ? 9. Measurability and continuity of representations, dynamical systems and homogeneous random fields.- ? 12. The Banach convergence principle.- ? 13. Directions and nets.- ? 14. Correspondence between left and right objects and conditions.- References....

Sommaire:
1: Means and averageable functions.- 2: Ergodicity and mixing.- 3: Averaging sequences. Universal ergodic theorems.- 4: Mean ergodic theorems.- 5: Maximal and dominated ergodic theorems.- 6: Pointwise ergodic theorems.- 7: Ergodic theorems for homogeneous random measures.- 8: Specific informational and thermodynamical characteristics of homogeneous random fields.- ? 1. Groups and semigroups.- ? 2. Homogeneous and group-type homogeneous spaces.- ? 3. Amenable semigroups and ergodic nets.- ? 4. Positive definite functions.- ? 5. Representations of semigroups in Banach spaces.- ? 6. Weakly almost periodic elements and functions.- ? 7. Dynamical systems.- ? 8. Homogeneous random functions.- ? 9. Measurability and continuity of representations, dynamical systems and homogeneous random fields.- ? 12. The Banach convergence principle.- ? 13. Directions and nets.- ? 14. Correspondence between left and right objects and conditions.- References.