When is the composition of functions measurable?
F. Javier Fern\'andez, F. Adri\'an F. Tojo
TL;DR
This paper investigates the conditions under which the composition of functions remains measurable, analyzing the necessity of certain assumptions and providing counterexamples to demonstrate the limits of these conditions.
Contribution
It establishes new criteria for the measurability of composed functions and demonstrates the sharpness of these conditions through counterexamples.
Findings
Identifies sufficient conditions for measurability of function composition.
Provides counterexamples showing the limits of weaker hypotheses.
Clarifies the role of interior function properties in measurability.
Abstract
In this article we explore under which conditions on the interior function the composition of functions is measurable. We also study the sharpness of the result by providing a counterexample for weaker hypotheses.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical Dynamics and Fractals