2 papers
math.CA2024
A Different Demonstration for Integral Identity Across Distinct Time Scales
Patrick Oliveira
In the theory of time scales, given a time scale with at least two distinct elements, an integration theory is developed using ideas already well known as Riemann sums…
math.PR2024
A Carathéodory's Extension Theorem for Families Simpler Than an Algebras of Sets
Patrick Oliveira
The Carathéodory's Extension Theorem is a powerful tool that allows us to generate a measure, over a sigma-algebra, from a pre-measure defined over an algebra of sets. However, al…