Summary
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.
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Dobrić, V. The law of large numbers in locally convex spaces. Probab. Th. Rel. Fields 78, 403–417 (1988). https://doi.org/10.1007/BF00334203
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DOI: https://doi.org/10.1007/BF00334203