CMIT | Pi Week Talk series, March 2026

Title: From Riemann to Henstock - Kurzweil : A Gauge Approach to Integration

Speaker: Praveen K C, IPhD25

Time & Date: 27th March 2026, 6:30 pm onwards
Venue: MSB Madhava

Abstract:The Henstock-Kurzweil integral, also known as the gauge integral, is a refinement of the classical Riemann integral that significantly enlarges the class of integrable functions while preserving a definition based on tagged partitions and Riemann sums. In this talk we introduce the notion of gauges and δ-fine partitions and use them to define Henstock-Kurzweil integrability on a compact interval. After establishing the existence of δ-fine partitions and discussing basic properties of the integral, we examine its relationship with classical theories of integration. In particular, we present a version of the Fundamental Theorem of Calculus in this setting, showing that every derivative is Henstock-Kurzweil integrable and that the integral recovers the increment of the primitive. The talk aims to illustrate how the gauge approach extends the Riemann integral while retaining a direct connection with classical analysis.