Probability Theory and Related Fields

, Volume 78, Issue 3, pp 403-417

First online:

The law of large numbers in locally convex spaces

  • V. DobrićAffiliated withDepartment of Mathematics, Lehigh University

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The law of large numbers is extended to random elements taking values in locally convex spaces. The necessary and sufficient conditions for the law are given in a large class of locally convex spaces, vix. ℱ normed spaces. This class includes, among others, the test function spaces and the distribution spaces.