Abstract
Let Φ be a compact set in a vector space equipped with a convergence which is metrizable in Φ but not certainly in the whole space. We endow the space of continuous on Φ linear functionals on span Φ with the norm \( {\left\| u \right\|_\Phi } = \sup \varphi \in \Phi \left| {u\varphi } \right| \) and call the elements of the completion of Φ hypermeasures. We prove theorems on the convergence in probability or in distribution and relative compactness in distribution of a sequence of random hypermeasures.
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Yurachkivsky, A. Convergence and relative compactness in distribution of sequences of random hypermeasures. Lith Math J 51, 587–600 (2011). https://doi.org/10.1007/s10986-011-9150-4
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DOI: https://doi.org/10.1007/s10986-011-9150-4