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Upper integral and its geometric meaning. (English) Zbl 1164.28003
The main idea of the paper is to study Hahn’s definition of the integral for non-measurable functions. The equivalence to the Fan integral is proved as well as Minkowski type inequality and Chebyshev inequality.
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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[1] FAN S. C.: Integration with respect to an upper-measure function. Amer. J. Math. 63 (1941), 319-337. · Zbl 0025.03401
[2] HAHN H.-ROSENTHAL A.: Set Functions. University of New Mexico Press, Albuquerque, 1948. · Zbl 0033.05301
[3] ROYDEN H. L.: Real Analysis. (3rd, Macmillan Publishing Company, New York, 1988. · Zbl 0704.26006
[4] TAYLOR A. E.: General Theory of Functions and Integration. Dover Publications Inc., New York, 1985.
[5] WARD A. J.: The Fan integrals interpreted as measures in a product-space. Amer. J. Math. 66 (1944), 144-160. · Zbl 0063.08175
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