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smirten
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hi, i am learing about measure theory and i am looking fore some good reference of the subjects ..
smirten said:hi, i am learing about measure theory and i am looking fore some good reference of the subjects ..
lavinia said:Royden; Real analysis
what applications are you interested in?
Measure theory is a branch of mathematics that deals with the concept of measuring sets and their properties. It provides a framework for understanding how to assign numbers to sets in a consistent and meaningful way.
Measure theory is important because it allows us to analyze and understand the behavior of sets in a rigorous and systematic manner. It is used in many areas of mathematics, including probability, analysis, and geometry, and has applications in fields such as physics, economics, and engineering.
Some key concepts in measure theory include measures, which assign numbers to sets in a consistent way; measurable sets, which are sets that can be assigned a measure; and integration, which allows us to calculate the area or volume of a set using measures.
A finite measure is a measure that assigns a finite number to a set, while an infinite measure assigns an infinite number to a set. In measure theory, we are often interested in studying infinite measures, as they allow us to analyze sets that may have an infinite number of elements.
Measure theory is closely related to probability, as it provides a mathematical foundation for understanding and analyzing random events. Probability can be seen as a special case of measure theory, where the measure is the probability of an event occurring. Many concepts in probability, such as expected value and variance, can be defined and studied using measure theory.