Integration of Sequences

Overview

In my research project I want to generalise the well-known concept of Riemann integration of functions on sequences in order to obtain a new tool for the investigation of sequences. To do this, I define an integral for sequences based on the Riemann integral and then investigate which sequences are integrable. I prove necessary and sufficient conditions for sequence integrability. It turns out that integrability for a sequence is a stronger condition than cesàro-convergence: Every integrable sequence is cesàro-convergent, but not every cesàro-convergent sequence is also integrable. As a sufficient criterion for integrability, we find a condition that ressembles to Lebesgue integration: If suitable preimages under the sequence are "measurable", meaning that we can assign them a kind of length, the sequence is integrable. For sequences with finitely many accumulation points, we prove that this criterion is also necessary.

Awards (4)

• Mu Alpha Theta, National High School and Two-Year College Mathematics Honor Society: First Award of $ 1,500 $1,500
• Fondazione Bruno Kessler: Award to participate in summer school "Web Valley"
• American Mathematical Society: One-Year Membership to American Mathematical Society to each winner (7 winning projects, up to 3 team members per project)
• American Mathematical Society: Second Award of $1,000 $1,000

Competition history

• ISEF 2024 Mathematics · Entry MATH012 · Los Angeles, California, United States Affiliated fair in Hamburg, Germany

Resources

• ISEF abstract page ↗

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