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A general concept in category theory involving the globalization of local morphisms.

If {f_n} is a sequence of measurable functions, with 0<=f_n<=f_(n+1) for every n, then intlim_(n->infty)f_ndmu=lim_(n->infty)intf_ndmu.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

A sequence {a_n} such that either (1) a_(i+1)>=a_i for every i>=1, or (2) a_(i+1)<=a_i for every i>=1.

A term in social choice theory meaning a change favorable for X does not hurt X.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

Moving medians are implemented in the Wolfram Language as MovingMedian[data, n].

A strong inequality in which a is not only less than b, but much less (by some convention) is denoted a<<b.

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.