Solutions

Chapter 1: Measures

§1.2: \sigma-Algebras

(#1) (#2) (#3) (#4) (#5)

§1.3: Measures

(#6) (#7) (#8) (#9) (#10) (#11) (#12) (#13) (#14) (#15) (#16)

§1.4: Outer Measures

(#17) (#18) (#19) (#20) (#21) (#22) (#23) (#24)

§1.5: Borel Measures on the Real Line

(#25) (#26) (#27) (#28) (#29) (#30) (#31) (#32) (#33)

Chapter 2: Integration

§2.1: Measurable Functions

(#1) (#2) (#3) (#4) (#5) (#6) (#7) (#8) (#9) (#10) (#11)

§2.2: Integration of Nonnegative Functions

(#12) (#13) (#14) (#15) (#16) (#17)

§2.3: Integration of Complex Functions

(#18) (#19) (#20) (#21) (#22) (#23) (#24) (#25) (#26) (#27) (#28) (#29) (#30) (#31)

§2.4: Modes of Convergence

(#32) (#33) (#34) (#35) (#36) (#37) (#38) (#39) (#40) (#41) (#42) (#43) (#44)

  1. John’s avatar

    Great job!

    Reply

  2. Dohyun’s avatar

    Really Meaningful Work!

    Reply

  3. Thanks’s avatar

    Thanks a lot for your hard work. It’s absolutely useless for grad students not to have solutions. Some may argue that students will cheat if they take a look at the solutions… I’m sorry, but if you’re in grad school and you’re “cheating” then you shouldn’t be in maths at all – it simply means you have no drive of your own, and must be herded like cattle to do your own work and learn. We owe no one HW or exams, but we owe it to ourselves to learn the subject, whichever way we see fit. HW and exams ought to be an AID to our learning, not a useless evaluation and appraisal by others (which is probably why we ought to get rid of them, especially in grad school!).

    Thanks for establishing this website, and I hope others take your lead. It’s absolutely important to learning to be able to see solutions after an honest attempt.

    Reply

  4. Bubby Brownose’s avatar

    When are you going to do the rest?

    Reply

  5. gwen’s avatar

    thanks a lot for the solution. really learned a lot!

    Reply

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