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Intuition for definition of Radon Measure

Measure on topological spacesInner regularity property of Radon measures in metric spacesIntuition behind the definition of a measurable setIntuition behind Gaussian isoperimetric inequalityAssumptions for definition of Radon measureSigma algebra on space of signed Radon measuresAbstracted Metric and Measure SpacesIs the dual space of all Radon measures the space of signed measures on a $delta$-ring?Construction of a Radon measure from a certain family of compact subsetsIntuition behind the direct integral of a family of Hilbert spacesStructure theorem for locally bounded variation functions

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According to the definition of the book "Measure Theory and fine properties of functions." -Evans Gariapery a measure u is said of Radon if they are worth the properties described in the attached image.

According to the Wiki the motivation for this definition is to find a way to measure sets of a topological space so that this way of measuring is compatible with the topology of space.

In simple terms, what precisely would "find a measure that is compatible with the topology?" Answering this question gives the intuition behind Radon's definition of measurement?

measure-theory geometric-measure-theory

share|cite|improve this question

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I can't figure out what you're asking.
  $endgroup$
  – Yanko
  Mar 15 at 18:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This asks a similar question. The accepted answer may be helpful.
  $endgroup$
  – John Douma
  Mar 15 at 18:58
  

  
  
  
  

add a comment | 

0

$begingroup$

According to the definition of the book "Measure Theory and fine properties of functions." -Evans Gariapery a measure u is said of Radon if they are worth the properties described in the attached image.

According to the Wiki the motivation for this definition is to find a way to measure sets of a topological space so that this way of measuring is compatible with the topology of space.

In simple terms, what precisely would "find a measure that is compatible with the topology?" Answering this question gives the intuition behind Radon's definition of measurement?

measure-theory geometric-measure-theory

share|cite|improve this question

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I can't figure out what you're asking.
  $endgroup$
  – Yanko
  Mar 15 at 18:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This asks a similar question. The accepted answer may be helpful.
  $endgroup$
  – John Douma
  Mar 15 at 18:58
  

  
  
  
  

add a comment | 

$begingroup$

According to the definition of the book "Measure Theory and fine properties of functions." -Evans Gariapery a measure u is said of Radon if they are worth the properties described in the attached image.

According to the Wiki the motivation for this definition is to find a way to measure sets of a topological space so that this way of measuring is compatible with the topology of space.

In simple terms, what precisely would "find a measure that is compatible with the topology?" Answering this question gives the intuition behind Radon's definition of measurement?

measure-theory geometric-measure-theory

share|cite|improve this question

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

$endgroup$

share|cite|improve this question

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

share|cite|improve this question

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

asked Mar 15 at 18:19

C. JuniorC. Junior

670412

asked Mar 15 at 18:19

C. JuniorC. Junior

670412