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In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every cluster point is a subsequential limit, but not conversely. For example {-1,1,-1,1,...} has a subsequential limit -1, but -1 is not a cluster point. In first-countable spaces, the two concepts coincide.
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We prove that has a unique weak subsequential limit in.
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The results on the synchronisation of automaton with bounded delay established so far did not keep the property of being subsequential.
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This also applies to products already on order provided that such alternations can be made without subsequential changes being necessary in specifications already agreed.
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In a topological space, if every subsequence has a subsequential limit to the same point, then the original sequence also converges to that limit. This need not hold in more generalized notions of convergence, such as the space of almost everywhere convergence. The supremum of the set of all subsequential limits of some sequence is called the limit superior, or limsup. Similarly, the infimum of such a set is called the limit inferior, or liminf.
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Almost everywhere pointwise convergence on the space of functions on a measure space does not define the structure of a topology on the space of measurable functions on a measure space (although it is a convergence structure). For in a topological space, when every subsequence of a sequence has itself a subsequence with the same subsequential limit, the sequence itself must converge to that limit. But consider the sequence of so-called "galloping rectangles" functions. Let N = Floor(log2 n) and k = n mod 2N.
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Archived Archived Archived First place and the subsequential promotion was secured in October 2004 at Løgumkloster Stadion in an 11-2 win over Broager UIF/Boldklub Frem Egernsund who had already suffered relegation from the division at that point. The win meant the second consecutive promotion for Tønder SF since the club's relegation to Serie 4 in the 2002 season. Thus, in FC Sydvest 05's inaugural season, the 2005 season, its first team would compete in the DBU Jutland Serie 2 after adopting Tønder SF's sporting license; the club competing at highest level of the parent clubs. Tønder SF formerly spent multiple seasons in the Denmark Series (fourth highest division) and with two second places in 1977 and 1978 they even came close to reaching promotion to the third tier, which was then known as the Danish 3rd Division (today known as 2nd Division due to the introduction of the Danish Superliga which replaced the former 1st Division in 1991).
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