NEED HELP Measurable real valued functions

In summary, measurable real valued functions are mathematical functions that map inputs to real numbers and are important in fields such as physics and economics. Common examples include polynomial, trigonometric, and exponential functions. They are used in scientific research to make predictions and understand complex systems, but can also present challenges in finding accurate models and solutions.
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Need help with this - just had this on a test and this is driving me crazy - PLEASE HELP!

Let {[itex]f_{n}[/itex]} be a sequence of MEASURABLE real valued functions. Prove that there exists a sequence of positive real numbers {[itex]c_{n}[/itex]} such that [itex]\sum c_{n}f_{n}[/itex] converges for almost every x [itex]\in[/itex] [itex]\Re[/itex]

How is it possible for this to be true? Please help!
 
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What methods have you tried so far?
 

What are measurable real valued functions?

Measurable real valued functions are mathematical functions that map a set of inputs to a set of real numbers. These functions are considered measurable if they have certain properties, such as being able to be approximated by simpler functions and being able to be integrated over a set of inputs.

Why are measurable real valued functions important?

Measurable real valued functions are important in many fields of science, including physics, economics, and statistics. They allow us to mathematically model and analyze real-world phenomena, making them an essential tool for understanding and predicting the world around us.

What are some examples of measurable real valued functions?

Some common examples of measurable real valued functions include polynomial functions, trigonometric functions, and exponential functions. These functions can be measured and analyzed in various ways, such as finding their maximum and minimum values, calculating their derivatives, and integrating them over a given interval.

How are measurable real valued functions used in scientific research?

Measurable real valued functions are used in a wide range of scientific research, from studying physical systems to analyzing data in psychology and economics. They allow scientists to make predictions, test hypotheses, and understand complex systems in a quantitative and objective manner.

What are some challenges in working with measurable real valued functions?

One challenge in working with measurable real valued functions is finding appropriate models for complex systems. It can also be challenging to accurately measure and analyze data, as small errors can greatly affect the results. Additionally, some functions may not have closed-form solutions, making it difficult to find exact solutions or make precise predictions.

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