Lebesgue-Stieltjes integral

Lebesgue-Stieltjes integral

[lə′beg ′stēlt·yəs ‚int·ə·grəl]
(mathematics)
A Lebesgue integral of the form where φ is of bounded variation; if φ(x) = x, it reduces to the Lebesgue integral of ƒ(x); if φ(x) is differentiable, it reduces to the Lebesgue integral of ƒ(x)φ′(x).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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where [mathematical expression not reproducible] denote the memductances of memristors [mathematical expression not reproducible] is the Lebesgue-Stieltjes integral and [[eta].sub.j]([theta]) is nonnegative function of bounded variation on (-[infinity], 0], which satisfies [[integra].sup.0.sub.-[infinity]]d[[eta].sub.j]([theta]) = [l.sub.j] > 0.