"semilimits" meaning in English

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          "ref": "2015, Thuong Nguyen, Antonio Siconolfi, “Singularly Perturbed Control Systems with Noncompact Fast Variable”, in arXiv:",
          "text": "We study the asymptotic, as {\\epsilon} goes to 0, of the corresponding value functions, and show convergence, in the sense of weak semilimits, to sub and supersolution of a suitable limit equation containing the effective Hamiltonian.",
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          "ref": "2015, Thuong Nguyen, Antonio Siconolfi, “Singularly Perturbed Control Systems with Noncompact Fast Variable”, in arXiv:",
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