Any elementary-level text or notes on (i) measure theory? (ii) Lebesgue integration?

Question

I still have no background in measure theory or Lebesgue integration. So is there any elementary-level resource --- book, set of notes, tutorial paper, website, or online video lecture series --- which I can use for getting some knowledge of these fields?

Answer 1

This is an introductory video course on measure and integration by Prof.Inder Rana of IIT Bombay. There are total 40 lectures with each one almost of an hour. Also he uses his own book on measure and integration along with Paul Halmos's and Royden's as mentioned in @BAYMAX's answer.

The syllabus of the course as well as the references are mentioned in the link.

Answer 2

I would like to suggest three books which helped me-

1) Royden's Real Analysis,here in this it gives motivation towards the topic as well as illustrative text,nice examples,excercises.

2)Measure Theory and Integration by G. de Barra.

3)Paul Halmos,Measure theory.

Also there are some similar questions asked and may contain some references as per your requirement - Reference book on measure theory and here.

And some online notes here and here.

Hope this helps!