Constructing a premeasure on half open intervals

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The discussion focuses on constructing a premeasure on half-open intervals within the set of extended real numbers. The original poster seeks clarity in demonstrating the steps of this construction. There is a request for assistance in understanding the concept of a premeasure. Participants emphasize the importance of clearly outlining the construction process. The conversation aims to provide guidance on effectively presenting the steps involved in this mathematical task.
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I want to construct a premeasure on half open intervals in the set of extended real numbers and showing
the steps of construction clearly.
I know what is premeasure and half open interval of course, but I have problems with showing my steps clearly. Please help
 
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any idea?
 
What do you mean with a premeasure?
 
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