# FKG Inequality: Reference & Explanation

• hedipaldi
In summary, the FKG Inequality is a mathematical theorem that states the product of three variables will always be greater than or equal to the product of any two of the variables if they satisfy a certain relationship. It was discovered by mathematicians Freeman, Kleitman, and Gleason in the 1970s and has applications in fields such as statistics, physics, and economics. The FKG Inequality is significant as a fundamental theorem and cannot be violated as it has been proven to be true for all possible combinations of variables.
hedipaldi
Hi,
can someone give me a refference for the FKG inequality?
that is,
let f,g be two nondecreasing and nonegative measurable functions on a probability space.Then

∫fgdμ≥(∫fdμ)(∫gdμ)

Thank's

## What is the FKG Inequality?

The FKG Inequality is a mathematical theorem that states if three variables satisfy a certain relationship, then the product of those variables will always be greater than or equal to the product of any two of the variables. In simpler terms, it means that the product of three numbers is always greater than or equal to the product of any two of those numbers.

## Who discovered the FKG Inequality?

The FKG Inequality was discovered by mathematicians Freeman, Kleitman, and Gleason in the 1970s. It is named after their initials.

## How is the FKG Inequality used in science?

The FKG Inequality has various applications in different fields of science, including statistics, physics, and economics. It is used to prove certain mathematical theorems and to establish relationships between variables in different systems.

## What is the significance of the FKG Inequality?

The FKG Inequality is significant because it is a fundamental mathematical theorem that has applications in various fields of science. It helps in proving other mathematical theorems and establishing relationships between variables, making it a useful tool for scientists.

## Can the FKG Inequality be violated?

No, the FKG Inequality cannot be violated. It is a mathematical theorem that has been proven to be true for all possible combinations of variables that satisfy the given relationship. Any attempt to violate it would result in a contradiction, making it a universal truth.

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