Difference between revisions of "Notes:Measures"

From Maths
Jump to: navigation, search
(Created page with "==Problem== It seems no one can agree on quite ''what'' a measure is. This page is intended to be a gathering of opinions from a few authors to see what is what. Bogachev for...")
 
(Proposal: non-monotone terminology)
Line 26: Line 26:
 
==Proposal==
 
==Proposal==
 
TODO!
 
TODO!
 +
 +
As for me, one usually says "measure" for a sigma-additive function with values in {{M|[0,\infty]}} on a sigma-algebra. For other cases, one adds something. Yes, I know, you hate this "non-monotone terminology", and I can understand your feeling, but I doubt we can change the world...
 +
 +
Namely, one says: "measure on algebra"; "signed measure"; "complex measure"; "vector measure"; "finitely additive measure". All these are not really measures. [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 21:19, 20 March 2016 (UTC)
 +
 +
(Is it OK to put here a signed message? This is not a talk page; but this is a note page...)
 +
 
[[Category:Measure Theory]]
 
[[Category:Measure Theory]]

Revision as of 21:19, 20 March 2016

Problem

It seems no one can agree on quite what a measure is. This page is intended to be a gathering of opinions from a few authors to see what is what. Bogachev for example (author of Books:Measure Theory - Volume 1 - V. I. Bogachev) doesn't require that a measure even be positive! Books used:

  1. Books:Measures, Integrals and Martingales - René L. Schilling
  2. Books:Real and Abstract Analysis - Edwin Hewitt & Karl Stromberg
  3. Books:Measure Theory - Volume 1 - V. I. Bogachev
  4. Books:Measure Theory - Paul R. Halmos
  5. Books:Analysis - Part 2: Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis - Krzysztof Maurin

Definitions

Bogachev

No notion of pre-measure

Measures, Integrals and Martingales

Maurin

Not applicable (not sure what magic he's up to....)

Halmos

Real and Abstract Analysis

Proposal

TODO!

As for me, one usually says "measure" for a sigma-additive function with values in [ilmath][0,\infty][/ilmath] on a sigma-algebra. For other cases, one adds something. Yes, I know, you hate this "non-monotone terminology", and I can understand your feeling, but I doubt we can change the world...

Namely, one says: "measure on algebra"; "signed measure"; "complex measure"; "vector measure"; "finitely additive measure". All these are not really measures. Boris (talk) 21:19, 20 March 2016 (UTC)

(Is it OK to put here a signed message? This is not a talk page; but this is a note page...)