Discrete orthogonal polynomials are orthogonal with respect to some discrete measure.
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Second, absolutely continuous measures are classified by the Radon Nikodym theorem, and discrete measures are easily understood.
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The simplest example of a discrete measure on the real line is the Dirac delta function \ delta.
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Technically the simplest examples are when " X " is a countable set and ? is a discrete measure.
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Rep . Nancy Johnson, R-Conn ., will introduce the child-support provisions of the welfare bill as a discrete measure this week.
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Geometrically, a discrete measure ( on the real line, with respect to Lebesgue measure ) is a collection of point masses.
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(1 ) The complex functions or a set of discrete measured data can be interpolated by a sum of polynomial or trigonometric function series.
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Thinking of curvature as a measure, rather than as a function, Descartes'theorem is Gauss Bonnet where the curvature is a discrete measure, and Gauss Bonnet for measures generalizes both Gauss Bonnet for smooth manifolds and Descartes'theorem.
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In fact, one may prove that any discrete measure on the real line has this form for appropriately chosen sequences s _ 1, s _ 2, \ dots and a _ 1, a _ 2, \ dots
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