Opinion about an introduction of the Lebesgue integral in "Introduction to Hilbert spaces with applications"

[Cauer]

I am an undergraduate student in physics. I wanted to deepen in the theory of Hilbert spaces and I took the book "Introduction to Hilbert spaces with applications" of Debnath and Mikusinski. I am writing this thread to know the opinion of the readers about the method of introducing the Lebesgue integral that one can find in the above-mentioned book. I don't have knowledgement of measure theory. The program in the bachelor's degree in physics is so short in the mathematical aspect! For someone who has worked the book, is "correct" the method for arriving to the Lebesgue integral?

Regards,

 

[fresh_42]

I am an undergraduate student in physics. I wanted to deepen in the theory of Hilbert spaces and I took the book "Introduction to Hilbert spaces with applications" of Debnath and Mikusinski. I am writing this thread to know the opinion of the readers about the method of introducing the Lebesgue integral that one can find in the above-mentioned book. I don't have knowledgement of measure theory. The program in the bachelor's degree in physics is so short in the mathematical aspect! For someone who has worked the book, is "correct" the method for arriving to the Lebesgue integral?

Regards,

While you are waiting for someone who has exactly this one book, you could read
https://www.physicsforums.com/insights/omissions-mathematics-education-gauge-integration/