Integral, Measure and Derivative: A Unified Approach by Shilov

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SUMMARY

The book "Integral, Measure and Derivative: A Unified Approach" by Shilov is highly regarded for its clarity and suitability for self-study, particularly for those interested in measure theory. It is recommended to be used alongside Kreyszig's "Functional Analysis," which is noted for its clear explanations. Additionally, the discussion mentions Cohn's text on Measure Theory as a potential follow-up, although it is described as less engaging compared to Shilov's work. Overall, Shilov's book is an excellent resource for learners seeking a solid foundation in measure theory.

PREREQUISITES
  • Familiarity with basic concepts of measure theory
  • Understanding of functional analysis principles
  • Knowledge of mathematical writing styles and clarity
  • Experience with self-study techniques in advanced mathematics
NEXT STEPS
  • Explore "Functional Analysis" by Kreyszig for foundational concepts
  • Study "Measure Theory" by Cohn for a comparative understanding
  • Research additional resources on measure theory for diverse perspectives
  • Investigate online courses or lectures on measure theory for guided learning
USEFUL FOR

Students and self-learners in mathematics, particularly those focusing on measure theory and functional analysis, will benefit from this discussion. It is also valuable for educators seeking clear instructional materials.

jmjlt88
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Greetings!

Can anyone tell me a little bit about the book Integral, Measure and Derivative: A Unified Approach by Shilov? Is it suitable for self-study? I am wishing to study the basics of measure theory. I will be using the text alongside Kreyszig's Funcational Analysis. Having already started the Kreyszig text, I can comment that it is crystal clear! As such, I am looking for a text at a similar level of difficulty (or written at the same level of clarity). Thank you for the input.


https://www.amazon.com/dp/0486635198/?tag=pfamazon01-20

P.S. I also purchased Cohn's text on Measure Theory. I have skimmed it; it seems "alright." I would maybe like to use that text as a follow up.
 
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Frankly, I haven't. However, I have read several of his other works (Elementary Real and Complex Analysis, Linear Algebra, Elementary Functional Analysis), and so I can attest to the superb quality of his writting.
 

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