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tunaaa
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Is it possible that 2 sigma-algebras could be independent under one measure but not independent under another?
Many thanks.
Many thanks.
tunaaa said:Is it possible that 2 sigma-algebras could be independent under one measure but not independent under another?
Many thanks.
chiro said:Hey tunaaa and welcome to the forums.
I don't know much about measure theory so maybe you could give us the definition of independence for a measure. I've heard about decomposing measures into orthogonal parts but I don't think this is what you are asking about.
Independence refers to the state of being free from outside control or influence. In scientific terms, it is the absence of a relationship or connection between two variables.
The concept of independence is often used in statistical analysis to assess the relationship between two variables. It is important to determine if the variables are independent of each other in order to accurately interpret the results of a study or experiment.
No, independence cannot be directly measured as it is a concept that describes the absence of a relationship between variables. However, statistical tests and measures can be used to determine the level of independence between variables.
Not necessarily. While independence is important in some types of research, there are also cases where variables may be related and studying this relationship is the main focus of the study. In these cases, independence is not desirable.
Researchers can ensure independence in their studies by carefully selecting and measuring variables, using appropriate statistical tests, and controlling for any potential confounding factors that could influence the results.