The concept of measure is a generalization of the concept of "length", "area" and "volume". The famous theory of measure would be the Lebesgue measure which associated to the Lebesgue integration.
Every definition of an integral in based on a particular measure. I never learned such integration is integrated with a particular measure. I mean not in a normal integration.
For example,
1. Riemann integral is based on Jordan measure
2. Lebesgue (pronounced ləˈbɛg) integral is based on Lebesgue measure.
These two famous integrals usually encounter when study of analysis of functions (reals or complex). Lebesgue integral for example plays an important role in the branch of mathematics called real analysis and in many other fields in the mathematical sciences.
Remark: The study of measures and their application to integration is known as measure theory.
Every definition of an integral in based on a particular measure. I never learned such integration is integrated with a particular measure. I mean not in a normal integration.
For example,
1. Riemann integral is based on Jordan measure
2. Lebesgue (pronounced ləˈbɛg) integral is based on Lebesgue measure.
These two famous integrals usually encounter when study of analysis of functions (reals or complex). Lebesgue integral for example plays an important role in the branch of mathematics called real analysis and in many other fields in the mathematical sciences.
Remark: The study of measures and their application to integration is known as measure theory.
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