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In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes.〔.〕 It serves as an instructive and useful precursor of the Lebesgue integral. ==Definition== The Riemann–Stieltjes integral of a real-valued function ''f'' of a real variable with respect to a real function ''g'' is denoted by : and defined to be the limit, as the mesh of the partition : of the interval () approaches zero, of the approximating sum : where ''c''''i'' is in the ''i''-th subinterval (). The two functions ''f'' and ''g'' are respectively called the integrand and the integrator. The "limit" is here understood to be a number ''A'' (the value of the Riemann–Stieltjes integral) such that for every ''ε'' > 0, there exists ''δ'' > 0 such that for every partition ''P'' with mesh(''P'') < ''δ'', and for every choice of points ''c''''i'' in (), : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Riemann–Stieltjes integral」の詳細全文を読む スポンサード リンク
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