closure
♦
9 matching pages ♦
(0.001 seconds)
9 matching pages
1: 1.4 Calculus of One Variable
…
►A generalization of the Riemann integral is the Stieltjes integral
, where is a nondecreasing function on the closure of , which may be bounded, or unbounded, and is the Stieltjes measure.
…
►For nondecreasing on the closure
of an interval , the measure is absolutely continuous if is continuous and there exists a weight function
, Riemann (or Lebesgue) integrable on finite subintervals of , such that
…
►where the supremum is over all sets of points in the closure of , that is, with added when they are finite.
…
►If is continuous on the closure of and is continuous on , then
…
2: 13.9 Zeros
…
►Let denote the closure of the domain that is bounded by the parabola and contains the origin.
…
3: 3.7 Ordinary Differential Equations
…
►Let be a finite or infinite interval and be a real-valued continuous (or piecewise continuous) function on the closure of .
…
►If is on the closure of , then the discretized form (3.7.13) of the differential equation can be used.
…
4: 1.9 Calculus of a Complex Variable
…
►Also, the union of and its limit points is the closure of .
…
5: 13.7 Asymptotic Expansions for Large Argument
…
►
…
6: 18.2 General Orthogonal Polynomials
…
►It is assumed throughout this chapter that for each polynomial that is orthogonal on an open interval the variable is confined to the closure of
unless indicated otherwise. (However, under appropriate conditions almost all equations given in the chapter can be continued analytically to various complex values of the variables.)
…
►More generally than (18.2.1)–(18.2.3), may be replaced in (18.2.1) by , where the measure is the Lebesgue–Stieltjes measure corresponding to a bounded nondecreasing function on the closure of with an infinite number of points of increase, and such that for all .
…
7: 2.10 Sums and Sequences
…
►
(a)
…
On the strip , is analytic in its interior, is continuous on its closure, and as , uniformly with respect to .
8: 1.16 Distributions
…
►The closure of the set of points where is called the support of .
…