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In mathematics, specifically in order theory and functional analysis, a **band** in a vector lattice is a subspace of that is solid and such that for all such that exists in we have ^{[1]}
The smallest band containing a subset of is called the **band generated by ** in ^{[1]}
A band generated by a singleton set is called a **principal band**.

For any subset of a vector lattice the set of all elements of disjoint from is a band in ^{[1]}

If () is the usual space of real valued functions used to define Lp spaces then is countably order complete (that is, each subset that is bounded above has a supremum) but in general is not order complete.
If is the vector subspace of all -null functions then is a solid subset of that is *not* a band.^{[1]}

The intersection of an arbitrary family of bands in a vector lattice is a band in ^{[2]}