Gauge Integrals over Metric Measure Spaces

The main aim of this work is to explore the gauge integrals over Metric Measure Spaces, particularly the McShane and the Henstock-Kurzweil integrals. We prove that the McShane-integral is unaltered even if one chooses some other classes of divisions. We analyze the notion of absolute continuity of charges and its relation with the Henstock-Kurzweil integral. A measure theoretic characterization of the Henstock-Kurzweil integral on finite dimensional Euclidean Spaces, in terms of the full variational measure is presented, along with some partial results on Metric Measure Spaces. We conclude this manual with a set of questions on Metric Measure Spaces which are open for researchers.

is working as an Assistant Professor at Department of Mathematics, Guru Nanak Dev University, Amritsar, India. He is a university topper in his Bachelors and Masters, recipient of Prestigious NBHM Scholarships and four academic Medals. He earned his PhD from Indian Institute of Technology, Bombay and specializes in Real Analysis.