A measure theoretic approach to logical quantification
We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This 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.
A new criterion of asymptotic periodicity of Markov operators on , established in [3], is extended to the class of Markov operators on signed measures.