Measure, Integration & Real Analysis

Sheldon Axler

errata

I tried hard to make Measure, Integration & Real Analysis error-free, but spotting mistakes in one's own writing can be difficult in a book-length work. All typos in the print version that I know about are listed below. These typos have all been corrected in the current electronic version dated 7 May 2021 (freely available here). The electronic version of the book available from Springer and on several other websites is older and does not include corrections to the typos below.

• page 4, line 5: “set” should be “nonempty set”. (corrected 9 July 2020)

• page 6, line 7 from bottom: “the first equality” should be “the equality”. (corrected 3 September 2020)

• page 18, line2 of second bullet point of 2.11: “[2, ∞]” should be “[2, ∞)”. (corrected 3 September 2020)

• page 23, lines 8 and 10: “D” should be “V ”. (corrected 1 June 2020)

• page 47, line 3: “A, B ∈ R” should be “A, B ⊂ R”. (corrected 22 September 2020)

• page 65, first line of 2.89: “measure space” should be “measurable space”. (corrected 1 June 2020)

• page 65, displayed equation defining f_k (x): “−k < f (x)” should be “−k ≤ f (x)” and “f (x) ≤ −k” should be “f (x) < −k”. (corrected 25 August 2020)

• page 66, line 10 from bottom: “=” should be “⊂ ”. (corrected 7 October 2020)

• page 85, Exercise 8: “Given” should be “Give”. (corrected 21 July 2020)

• page 91, lines 2 and 9 from bottom: “inf f ” should be “inf g ”. (corrected 21 July 2020)

• page 115, Exercise 6: “h = 0” should be “h(s) = 0 for almost every s ∈ R”. (corrected 8 August 2020)

• page 168, first line of proof of 6.46: “then” should be “Then”. (corrected 26 January 2021)

• page 251, Exercise 7: “space” should be “space V and f ∈ V ”. “converges” (twice) should be “equals f ”. “injective” should be “injective and surjective”. (corrected 22 March 2021)

• page 252, Exercise 11: Add the hypothesis that Γ is a countable set. (corrected 24 March 2021)

• page 274, line 10 from bottom: “Refine” should be “Redefine”. (corrected 21 August 2020)

• page 284, line 3 from bottom: “Tg” should be “Tf ”. (corrected 1 June 2020)

• page 290, line 5 from bottom: “such” should be “such that”. (corrected 6 April 2021)

• page 313, last line of text box at top of page: “nor V ” should be “nor B(V) ”. (corrected 1 February 2021)

• page 321, line 12 from bottom: “T - αf ” should be “T - αI ”. (corrected 1 June 2020)

• page 340, line 4 from bottom: “(π, π]” should be “(-π, π]”. (corrected 26 April 2021)

• page 348, Definition 11.19: Each “f ” should be “u”. (corrected 1 May 2021)

• page 351, line 4 from bottom: “each” should be “each z”. (corrected 30 April 2021)

• page 362, Exercise 11: A factor of 1/(2πi) is missing from right side of displayed equation. (corrected 1 June 2020)

• page 362: The last line of Exercise 13 should be “that if f ∈ L¹(∂D), then f ∗ g ≠ g.” (corrected 1 June 2020)

• page 365, line 11: “|e^iθ -1| ≤ θ” should be “|e^iθ -1| ≤ |θ|”. (corrected 7 May 2021)

• page 377, second to last paragraph of proof of 11.87: “Part (a)” should be “Part (b)”. (corrected 1 June 2020)

• page 388, line 4: “|f_n(t)| ≤ t ” should be “|f_n(t)| ≤ |t| ”. (corrected 30 July 2020)

If you notice additional errors in the book or have suggestions for improvements, please let me know by sending an email message to measure@axler.net.

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