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
Because limV is not universally standardized, readers should consult the specific source for the precise definition
See also: Limit, Convergence, Vector-valued function, Sequence, Net.