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.
Citation
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
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