Real Analysis
by H. L. Royden, Patrick Fitzpatrick, Halsey Royden, Royden, ROYDEN & FITZPATRICK · first published 1963
67% recommend33% neutral
Ben shu zhu yao fen san bu fen:di yi bu fen wei shi bian han shu lun, Di er bu fen wei chou xiang kong jian, Di san bu fen wei yi ban ce du yu ji fen lun.
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2009–2025Real and complex analysis
Walter Rudin
Recommended by 25 · mentioned by 4025 recommend · 40 mention25 recommend · 4025 recommend
2009–2025Mathematical foundations of the calculus of probability
J. Neveu
Recommended by 3 · mentioned by 63 recommend · 6 mention3 recommend · 63 recommend
2009–2023A Course in Probability Theory
Kai Lai Chung
Recommended by 3 · mentioned by 73 recommend · 7 mention3 recommend · 73 recommend
2008–2026Principles of Mathematical Analysis
Walter Rudin
Recommended by 52 · mentioned by 8852 recommend · 88 mention52 recommend · 8852 recommend
2010–2018Measure theory
Paul R. Halmos
Recommended by 2 · mentioned by 42 recommend · 4 mention2 recommend · 42 recommend
2009–2026Finite-dimensional vector spaces
Paul R. Halmos
Recommended by 24 · mentioned by 3824 recommend · 38 mention24 recommend · 3824 recommend
2008–2021Brownian motion and stochastic calculus
Ioannis Karatzas, Steven E. Shreve
Recommended by 3 · mentioned by 63 recommend · 6 mention3 recommend · 63 recommend
2009–2024Functions of Several Variables
Wendell Fleming, W. H. Fleming
Recommended by 4 · mentioned by 54 recommend · 5 mention4 recommend · 54 recommend
…rational and 0 otherwise. Then the Riemann integral of f over [0,1] does not exist, but the measure theory integral does and gives 0 for the result. There are at least two now classic books, Royden, Real Analysis and Rudin, Real and Complex Analysis. But there are more, and likely more can be written. For Rudin, can f'get about the last half on functions of a complex variable. Royden is easier to read. Rudin…
on “Why squared error? (2014)” ↗Suggestion: Set aside complex variables and do measure theory instead. For the Fourier and Laplace transforms, cover those via measure theory. For measure theory, H. Royden, Real Analysis and the first half of W. Rudin, Real and Complex Analysis. Then take a course in graduate probability which is based on measure theory. Good authors are Loeve, Neveu, Breiman, Chung, among others.…
on “Self Studying the MIT Applied Math Curriculum” ↗…done; learn some more material important in the rest of mathematical analysis. Spivak, Calculus on Manifolds The three above were at one time the main references for Harvard's famous Math 55. Royden, Real Analysis Measure theory and a start on functional analysis. Elegant. Rudin, Real and Complex Analysis Rock solid, measure theory again, and more on functional analysis. Also von Neumann's cute proof of the…
on “What's a Mathematician to do?” ↗…book is available in English now). It may be that you are not interested in relativity theory or the rest of mathematical physics -- fine, and that can help you set aside some topics. Then, Royden, Real Analysis and the first half of Rudin's R&CA as above, along with any of several alternatives, cover measure theory and the beginnings of functional analysis. Measure theory does calculus again and in a more powerful…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗…Measure Theory is a good prerequisite to Neveu. Rudin, Principles is a bit too little. Instead, the first half, the real half of Rudin's Real and Complex Analysis is a good prerequisite. So, is Royden's Real Analysis. Neveu is elegant beyond belief, but Breiman, Probability, the SIAM book, available in paperback, is darned good, usually easier than Neveu, less elegant, closer to applications, and without some of…
on “How to learn data science” ↗…approximate functions by other functions, e.g., how to approximate random variables by other random variables, e.g., learn Fourier theory), but for that also should have measure theory, e.g., from Royden, Real Analysis and/or the first half of Rudin, Real and Complex Analysis. For that, as in Math 55, a prerequisite is Rudin's, Principles. Rudin's Functional Analysis is more advanced, still. I got accepted to grad school…
on “The best linear algebra books” ↗…some phone calls for a list of recommended texts. One of those might be W. Rudin, Principles of Mathematical Analysis. aka, "Baby Rudin". It's highly precise and challenging. For more, H. Royden, Real Analysis W. Rudin, Real and Complex Analysis L. Breiman, Probability M. Loeve, Probability J. Neveu, Mathematical Foundations of the Calculus of Probability The last two are challenging. For Bayesian, that's…
on “Ask HN: What maths are critical to pursuing ML/AI?” ↗…a lot of mathematical analysis as a prerequisite, and the standard is Rudin's Principles. Then need quite a lot of measure theory and then some functional analysis. For that, the nicest is Royden's Real Analysis, but I also like the first (real) half of Rudin's Real and Complex Analysis. Then for the probability, sure, Loeve, Neveu, and Breiman. Loeve was long at Berkeley and wrote the big book. His writing…
on “Probability Theory Review for Machine Learning” ↗…especially good. Cinlar does not mention measure theory, but other texts do or really are all about measure theory, that is probability based on measure theory. Can get the measure theory out of Royden, Real Analysis and Rudin, Real and Complex Analysis. Should have a measure theory background in probability, and for that try any or all of Breiman, Neveu, Loeve, Chung. Can get into potential theory. Then stochastic…
on “Introduction to Probability for Data Science” ↗…take a detour into differential geometry so that can see why Rudin, Fleming, etc. do exterior algebra, and why Halmos does multi-linear algebra, and then will have a start on general relativity. Royden, Real Analysis. So will learn measure theory, crucial for good work in probability and stochastic processes, and get a start on functional analysis (vector spaces where each point is a function -- good way to see how…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗…Spivak, Calculus on Manifolds were the three main texts for Harvard's famous Math 55. Get good with proving the theorems. I also recommend Fleming, Functions of Several Variables. Then, sure, Royden, Real Analysis. Couldn't be prettier. If not in a hurry, then the real half of Rudin's Real and Complex Analysis. Especially if you like Fourier theory! Then of the probability books, I believe that the nicest, first book…
on “Foundations of probability theory” ↗…used, and pay whatever you have to. This way get to see the 2-3 dimensional versions and, really, mostly enough for what physics and engineering do with vector analysis and Stokes theorem. In H. Royden, Real Analysis and the first half of W. Rudin, Real and Complex Analysis, can see the Lebesgue integral, due to H. Lebesgue near 1900. In essentially all cases where the Riemann integral is defined, the Lebesgue integral is…
on “Ask HN: How to self-study mathematics from the undergrad through graduate level?” ↗…probability and stochastic processes -- E[X] is just Lebesgue's integral generalization of the calculus Riemann integral. Long standard very careful, polished, treatments of measure theory are in Royden, Real Analysis and the first half of Rudin, Real and Complex Analysis. Continuing with probability is Breiman, Probability, Neveu, Mathematical Foundations of the Calculus of Probability, Loeve, Probability, etc.…
on “Gaussian Processes, not quite for dummies” ↗…theory, the Lebesgue integral, Fourier theory, Hilbert space and Banach space as in, say, the first, real (not complex) half of Rudin, Real and Complex Analysis But for that I would start with Royden, Real Analysis sweetheart writing on that math. Depending on the math department, those books might be enough to pass the Ph.D. qualifying exam in Analysis. It was for me: From those books I did the best in the…
on “Ask HN: Recommend a maths book for a teenager?” ↗…Halmos, Finite Dimensional Vector Spaces, W. Rudin, Principles of Mathematical Analysis, Neveu, Mathematical Foundations of the Calculus of Probability, E. Nering, Linear Algebra and Matrix Theory, Royden, Real Analysis where do a lot of the exercises as homework and where the professor DOES read and remark on your writing. Neveu was a Loeve student at Berkeley. Nering was an Artin student at Princeton. As I recall,…
on “Three sins of authors in computer science and math (1997)” ↗