Almost Everywhere First-Return Recovery
Copyright policy )Almost Everywhere First-Return Recovery
The most important results of this paper are as follows: A function \(f:I\rightarrow \mathbb{R}\) is measurable iff it is a.e. recoverable. A function \(f:I\rightarrow \mathbb{R}\) has the Baire property iff it is recoverable except at a first category set of points. The first result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.
- University of St Andrews United Kingdom
- Washington and Lee University United States
- St. Olaf College United States
Baire property of function, trajectory, Lebesgue measurable functions, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence, Integrals of Riemann, Stieltjes and Lebesgue type, Classical measure theory, trajectory first-return yields Lebesgue integral
Baire property of function, trajectory, Lebesgue measurable functions, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence, Integrals of Riemann, Stieltjes and Lebesgue type, Classical measure theory, trajectory first-return yields Lebesgue integral
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