Here are some solutions to exercises in the book: Measure and Integral, An Introduction to Real Analysis by Richard L. Wheeden and Antoni Zygmund.
Chapter 1,2: analysis1
Chapter 3: analysis2
Chapter 4, 5: analysis3
Chapter 5,6: analysis4
Chapter 6,7: analysis5
Chapter 8: analysis6
Chapter 9: analysis7
Other than this book by Wheedon, also check out other highly recommended undergraduate/graduate math books.
Books to Transition from Math to Data Science
Graduating soon and interested to transition to data science (dubbed the sexiest job of the 21st century)? We recommend two books which are very suitable for students with strong math background, but little or no background in data science/ machine learning.
Do check out the following data science / machine learning book (rated 4.5/5 on Amazon) Pattern Recognition and Machine Learning (Information Science and Statistics) which is an in-depth book on the fundamentals of machine learning. The author Christopher M. Bishop has a PhD in theoretical physics, and is the Deputy Director of Microsoft Research Cambridge.
The above book is good for building a solid, theoretical foundation for a data scientist job. The next book Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems is ideal for learning hands-on practical coding for building machine learning (including deep learning) models. The author Aurélien Géron is a former Googler who was the tech lead for YouTube video classification.
Do you know how to prove sin(1/x)/x is not Lebesgue Integrable on (0,1]?
Also check out other popular Measure Theory exam question topics here:
- Questions related to Lebesgue Measure
- Fatou’s Lemma for Convergence in Measure
- Fatou’s Lemma
- Sufficient condition for Weak Convergence
- Generalized Lebesgue Dominated Convergence Theorem Proof
- The most Striking Theorem in Real Analysis
- Lusin’s Theorem and Egorov’s Theorem
- Arzela-Ascoli Theorem and Applications
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