Vol. 49, No. 2, 1973

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Bounds for products of interval functions

Jon Craig Helton

Vol. 49 (1973), No. 2, 377–389
Abstract

Since it is possible for aΠb(1 + G) to exist and not be zero when G is unbounded and 1 + G. is not bounded away from zero, the conditions under which products of the form |Π1n[1 + G(xq1,xq)]| are bounded or bounded away from zero for suitable subdivisions {xq}0n of [a,b] are important in many theorems concerning product integrals. Conditions are obtained for such bounds to exist for products of the form Π(1 + FG) and Π(1 + F + G), where F and G are functions from R × R to R. Further, these results are used to obtain an existence theorem for product integrals.

Mathematical Subject Classification 2000
Primary: 28A10
Milestones
Received: 10 May 1972
Published: 1 December 1973
Authors
Jon Craig Helton