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2013 The Gauge Integral Theory in HOL4
Zhiping Shi, Weiqing Gu, Xiaojuan Li, Yong Guan, Shiwei Ye, Jie Zhang, Hongxing Wei
J. Appl. Math. 2013(SI10): 1-7 (2013). DOI: 10.1155/2013/160875

Abstract

The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. In this paper, we formalize the operational properties which contain the linearity, monotonicity, integration by parts, the Cauchy-type integrability criterion, and other important theorems of the gauge integral in higher-order logic 4 (HOL4) and then use them to verify an inverting integrator. The formalized theorem library has been accepted by the HOL4 authority and will appear in HOL4 Kananaskis-9.

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Zhiping Shi. Weiqing Gu. Xiaojuan Li. Yong Guan. Shiwei Ye. Jie Zhang. Hongxing Wei. "The Gauge Integral Theory in HOL4." J. Appl. Math. 2013 (SI10) 1 - 7, 2013. https://doi.org/10.1155/2013/160875

Information

Published: 2013
First available in Project Euclid: 9 May 2014

zbMATH: 1268.65033
MathSciNet: MR3049447
Digital Object Identifier: 10.1155/2013/160875

Rights: Copyright © 2013 Hindawi

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