limV

limV is a nonstandard notation used in a few mathematical texts to denote the limit of a vector-valued quantity. It is not part of a single formal operator; its meaning is defined by context. In common usage, limV v_n = v means that the sequence of vectors converges to v in the chosen vector space, which in normed spaces is equivalent to ||v_n - v|| -> 0. Alternatively, limV v(t) = v0 as t approaches t0 expresses the pointwise or topological limit of a vector-valued function; the precise mode of convergence depends on the underlying topology. In general, when limV is used with nets or filters, convergence is defined with respect to that topology.

Practical guidance: always specify the space, topology, and mode of convergence (norm, weak, etc.). If limV is defined for a sequence of vectors, specify the index set and convergence criterion; if it is for a function, specify the variable, limit point, and type of convergence.

Because limV is not universally standardized, readers should consult the specific source for the precise definition when encountering the symbol. It is more common in informal or context-specific discussions, and many authors prefer writing explicit limit expressions such as lim_{n→∞} v_n or lim_{t→t0} v(t) to avoid ambiguity.

See also: Limit, Convergence, Vector-valued function, Sequence, Net.