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edited Jun 15, 2020 at 7:27

Marc Rieffel has some notes that develop integration with respect to Banach-space valued measures from the ground up. The notes are very thorough. They are available here:

http://math.berkeley.edu/~rieffel/measinteg.html

Lectures notes from 1970 for the first-year graduate-level analysis course on measures and integration at UC Berkeley that I gave several times during the late 1960's can be found here. The notable feature of the notes is that they treat the Bochner integral from the beginning, in a quite elementary way (e.g. no mention of the Hahn-Banach theorem). This has both practical and pedagogical advantages. Not all lectures listed in the table of contents were ever typed up.

The origin of these lecture notes lies in the turmoil on the UC Berkeley campus in the late 1960's, when there were periods of time when students indicated that as a protest they did not want to come to class (and if they did try to come to class there was a significant probability that they would encounter tear-gas or worse), but they indicated that they wanted to continue their studies and so requested that written notes of the lectures they missed (if held at all) be made available to them.

Marc Rieffel has some notes that develop integration with respect to Banach-space valued measures from the ground up. The notes are very thorough. They are available here:

http://math.berkeley.edu/~rieffel/measinteg.html

Lectures notes from 1970 for the first-year graduate-level analysis course on measures and integration at UC Berkeley that I gave several times during the late 1960's can be found here. The notable feature of the notes is that they treat the Bochner integral from the beginning, in a quite elementary way (e.g. no mention of the Hahn-Banach theorem). This has both practical and pedagogical advantages. Not all lectures listed in the table of contents were ever typed up.

The origin of these lecture notes lies in the turmoil on the UC Berkeley campus in the late 1960's, when there were periods of time when students indicated that as a protest they did not want to come to class (and if they did try to come to class there was a significant probability that they would encounter tear-gas or worse), but they indicated that they wanted to continue their studies and so requested that written notes of the lectures they missed (if held at all) be made available to them.

Marc Rieffel has some notes that develop integration with respect to Banach-space valued measures from the ground up. The notes are very thorough. They are available here:

http://math.berkeley.edu/~rieffel/measinteg.html

Lectures notes from 1970 for the first-year graduate-level analysis course on measures and integration at UC Berkeley that I gave several times during the late 1960's can be found here. The notable feature of the notes is that they treat the Bochner integral from the beginning, in a quite elementary way (e.g. no mention of the Hahn-Banach theorem). This has both practical and pedagogical advantages. Not all lectures listed in the table of contents were ever typed up.

The origin of these lecture notes lies in the turmoil on the UC Berkeley campus in the late 1960's, when there were periods of time when students indicated that as a protest they did not want to come to class (and if they did try to come to class there was a significant probability that they would encounter tear-gas or worse), but they indicated that they wanted to continue their studies and so requested that written notes of the lectures they missed (if held at all) be made available to them.

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Marc Rieffel has some notes that develop integration with respect to Banach-space valued measures from the ground up. The notes are very thorough. They are available here:

http://math.berkeley.edu/~rieffel/measinteg.html

Lectures notes from 1970 for the first-year graduate-level analysis course on measures and integration at UC Berkeley that I gave several times during the late 1960's can be found here. The notable feature of the notes is that they treat the Bochner integral from the beginning, in a quite elementary way (e.g. no mention of the Hahn-Banach theorem). This has both practical and pedagogical advantages. Not all lectures listed in the table of contents were ever typed up.

The origin of these lecture notes lies in the turmoil on the UC Berkeley campus in the late 1960's, when there were periods of time when students indicated that as a protest they did not want to come to class (and if they did try to come to class there was a significant probability that they would encounter tear-gas or worse), but they indicated that they wanted to continue their studies and so requested that written notes of the lectures they missed (if held at all) be made available to them.