## Abstract

Let E and F be a pair of locally convex spaces in duality, with σ and τ the weak and Mackey topologies on E. A sequence of functions {f_{n}} on E is said to be Mosco-convergent to another function f_{0}, denoted f_{n} M → f_{0}, if for every v ε{lunate} E, lim sup_{n → t8} f_{n}(v_{n}) ≤ f_{0}(v) for some sequence v_{n} t → v, and lim inf_{n → ∞} f_{n}(v_{n}) ≥ f_{0}(v) for every sequence v_{n} δ → v. In this paper it is shown that if F is a separable Fréchet space, {f_{n}: n ≥ 1} a sequence of proper, lower semicontinuous convex functions, and f_{n}^{*} the convex conjugate of f_{n}, then f_{n} M → f_{0} ⇒ f^{*}_{n} M → f^{*}_{n} if f_{0}(v) < ∞ for some v ε{lunate} E.

Original language | English (US) |
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Pages (from-to) | 226-246 |

Number of pages | 21 |

Journal | Journal of Functional Analysis |

Volume | 110 |

Issue number | 1 |

DOIs | |

State | Published - Nov 15 1992 |

## ASJC Scopus subject areas

- Analysis