SIGNATURE WORK
CONFERENCE & EXHIBITION 2023

The Lebesgue differentiation theorem is a cornerstone result in measure theory that highlights the behavior of a measurable function’s average value around a point. We extend the theorem to consider nicely shrinking sets, broadening its applicability in various contexts. Furthermore, we delve into the geometry of the Kakeya Problem and the closely related Kakeya Conjecture, investigating the existence of Besicovitch sets and their properties. We provide a proof confirming the existence of these sets and explore their size in finite fields.