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Let be a locally compact Hausdorff space and let be the Banach space of all complex valued continuous functions vanishing at infinity in , provided with the supremum norm. Let be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of -valued -additive Baire measures on is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map when...
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
Given a two-dimensional fractional multiplicative process determined by two Hurst exponents and , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of by if and only if .
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