arXiv subjects

C. Bryan Dawson

Publications and source records attributed to C. Bryan Dawson.

2 recordsLinked to original sources

arXiv2018

Direct Proofs of the Fundamental Theorem of Calculus for the Omega Integral

When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow immediately, a much more satisfying approach would be to provide direct proofs not relying on the Riemann integral. This note provides those proofs.

math.CA↗

arXiv1994

On Convergence of Conditional Expectation Operators

Given an operator $T:U_X(Σ)\to Y$ or ${T:U(Σ)\to Y$, one may consider the net of conditional expectation operators $(T_π)$ directed by refinement of the partitions $π$. It has been shown previously that $(T_π)$ does not always converge to $T$. This paper gives several conditions under which this convergence does occur, including complete characterizations when $X={\bold R}$ or when $X\sp *$ has the Radon-Nikodým property.

math.FA↗