ISL Real Analysis & Measure Theory (2012)


Delhi University, Delhi

Dates: 26th Mar - 7th April 2012


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)


Ajay Kumar

Sanjay Kumar Pant

Mukund Madhav Mishra

Mailing Address

Coordinator, Professor,
Department of Mathematics,
University of Delhi.

Co-coordinator, Associate Professor,
Department of Mathematics,
DDU College,
University of Delhi.

Co-coordinator, Assistant Professor,
Department of Mathematics
Hans Raj College
University of Dehi.


Aim of this workshop is to provide an understanding of the theory of integration on measure spaces. The school will discuss Riemann's theory of integration and its deficiencies. This study would, at the same time, develop an understanding of integration as a limit of sums andestablish the requirement of a rather general theory of integration which may improve the Riemann's theory. After the introduction to Lebesgue measure and Lebesgue integral on R, the concept of measure space and measure integration would be studied.Topics such as Lp spaces and Riesz representation theorem are important from Functional analytic view point. An study of Riemann integration on R^n will be a starting point for the study of measure and integration on product spaces. The school will also emphasize deficiencies of Lebesgue integration which can be a motivation for the participants to study more general theories of integration such as Henstock and Kurzweil integral.

Speakers and Syllabus 


Speaker Lectures Detailed Syllabus
RK Panda, DU
6 Sequences and Series of Numbers and Functions, Uniform Convergence,
Power Series, Differentiation of Function of One Variable, Mean Value
Sanjay K Pant
6 Introduction to Riemann Integration, Riemann Integrable Functions,
Stieltje's Integration, Integration as inverse of Differentiation:Fundamental
Theorem of Integral Calculus, Dificiencies of Riemann Integration.
E K Narayanan,
IISc, Bangalore
6 Algebra and Sigma Algebra of Sets, Lebesgue Outer Measure on R,
Measurability of Sets; Lebesgue Measure on R, Borel Sets in R,
Integration of Simple and Positive Functions, Monotone Convergence
Theorem, Fatou's Lemma and Dominated Convergence Theorem,
Riemann and Lebesgue Integrals.
I K Rana, IIT
6 Measures and Outer Measures, Extension of a Measure, Completion of a
Measure, Measure Space, Integration With Respect to a Measure, Vector
Valued Measures and Integration of Vector Valued Functions.
Parasar Mohanty, IIT , Kanpur
6 Borel and Radon Mesasures, Riesz Representation Theorem, Regularity
Properties of Borel Measures, The Lp Spaces, Convex Function, Jensen's
Inequality, Minkowski's and Holder's Inequalities, Completeness of Lp
Ajay Kumar, DU
6 Riemann Integration in R^n, Measurability on Cartesian Products, Product
Measures, Fubini Theorem, Completion of Product Measures,
Convolutions of Functions.

Unity of Mathematics Lecture:
Rajinder Bhatia (RB) , ISI, Delhi
Dinesh shingh, DU, Delhi

Course Associates:

1. M. M. Mishra, Hans Raj College, DU

2. Gunjan Khurana, I. P. College, DU

3. Ashish Bansal, Keshav Mahavidyalay, DU




Selected Applicants

Following applicants are shortlisted to participate in the school. The selected participants are requested to confirm their participation by Feb 16, 2012 by sending an e-mail to mukund.math at In case a selected participant fails to send his/her confirmation, applicants from waiting list would be given a chance. No further request would be entertained.

S. No. Name of the selected participant Affiliation
1 Avijit Sarkar The University of Burdwan
2 Jagjit Singh Matharu Bebe Nanaki University College, Kapurthla
3 Pabitra Debnath St. Xavier's College, Kolkata
4 Snehal Mitragotri(F) Shivaji University, Kolhapur
5 B Surendranath Reddy SRTM University, Nanded
6 Hemlata Pande(F) Kumaun University, Almora
7 Jyoti R Thorwe(F) Shivaji University, Vidyanagar
8 Pawan Tamta Kumaun University, Almora
9 Nisar Ahmad Lone Kashmir University, Srinagar
10 K. B. Mangang Mizoram University, Aizawl
11 Manob Kumar Ghosh Dumkal College, Basantapur
12 Sameer Ahmad Gupkari Govt Degree College, Anantnag
13 Deepti Lohia(F) Guru Nanak College, Muktsar
14 Jino Nainan St.Gregorios College, Kollam
15 Brijesh Sharma University of Allahabad
16 Priyabrat Gochhayat Sambalpur University
17 Saidur R. Barbhuiya S.S.College, Hailakandi, Assam
18 Naba Kanta Sharma Assam University
19 Rameez Raja University of Kashmir
20 Mohd Rafiq Mirza Sultan ul Arifeen Hr Secondary, Kashmir
 Waiting List 
1 Joydeep Sengupta University of North Bengal
2 Ramdas B. Sonawane K. A. A. N. M. Sonawane Arts, Commerce & Science College, Satara
3 Vijender Challa Bankatlal Badruka College for Informationa Technology, Hyderabad
4 Rupali Jain(F) SRTM University, Nanded
5 Renjit Kumar Yesodharan MSM College, Kerala
6 Roy John St. Stephan's College, Pathanapuram
7 Kiran Virivinti Osmania University, Hyderabad

Participants from NCR

S. No. Name of the participant Affiliation
1 Ashish Bansal Keshav Mahavidyalay, Delhi
2 Sushil Kumar Goswami Bharati Vidyapeeth College of Engineering, Delhi
3 Aditya Bhan Ojha Directorate of Census Operations, Delhi
4 Thakur Prasad Pandey G. B. Pant Engineering College
5 Rajinder Kaur(F) Swami Shraddhanand College, Delhi
6 Ashesh Kumar Jharwal Shivaji College, Delhi
7 Monika Singh(F) Lady Shri Ram College, Delhi
8 Rakesh Batra Hans Raj College, Delhi
9 Pawan Kumar IGNOU, Delhi
10 Raj Kumar Kirori Mal College, Delhi
11 Devendra Kumar MMH College, Ghaziabad
12 Narender Kumar Gargi College, Delhi
13 Bhungba Maiban Khuman Kirori Mal College, Delhi
14 Harindri Chaudhary(F) Deshbandhu College, Delhi


How to reach


How to reach the venue: Reaching DU (Guest Houses)

Approximate Distances of Delhi University from

  • International Airport: 35 km
  • Airport, Domestic terminal: 30 km.
  • New Delhi Railway station: 10 km.
  • Delhi (old Delhi) Railway station: 5 km.
  • Hazrat Nizamuddin Railway station: 15 km.
  • Inter State Bus Terminal, Kashmere Gate: 3 km.
  • Rajghat: 6 km.

A : From Railway Station:

  1. The best way from New Delhi railway station & old Delhi railway station to reach above destinations, is to take metro to Delhi University (Station name-vishwavidhalya metrostation). Time: 10 to 12 min. For University Guest House, Intrnational Guest House take auto or rickshaw from Delhi University metro station (distance - 1 km).
  2. From Hazarat Nizamuddin railway station hire a prepaid taxi from the prepaid taxi/ Auto booth located outside (exit to Sarai Kale Khan side of the railway station) by paying the nominal amount fixed by the government (based on distance) and get down at the place of your accommodation.

B : From Airport :

  1. Prepaid taxi is the best option to reach any of the said guest houses/hostels from airport. Prepaid taxi booth is located just outside the airport premises. Just pay your taxi charge to the booth officer and hire a prepaid taxi. Do not pay any additional amount to the driver.