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If {f_n} is a sequence of nonnegative measurable functions, then intlim inf_(n->infty)f_ndmu<=lim inf_(n->infty)intf_ndmu. (1) An example of a sequence of functions for which ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

A subset G subset R of the real numbers is said to be a G_delta set provided G is the countable intersection of open sets. The name G_delta comes from German: The G stands ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

Suppose that A is a Banach algebra and X is a Banach A-bimodule. For n=0, 1, 2, ..., let C^n(A,X) be the Banach space of all bounded n-linear mappings from A×...×A into X ...

An indirectly conformal mapping, sometimes called an anticonformal mapping, is a mapping that reverses all angles, whereas an isogonal mapping can reverse some angles and ...

Jordan's lemma shows the value of the integral I=int_(-infty)^inftyf(x)e^(iax)dx (1) along the infinite upper semicircle and with a>0 is 0 for "nice" functions which satisfy ...