Köker SigmaCebir 1.0
A .NET application for checking sigma-algebra conditions over a finite sample space and helping identify missing closure sets.
Köker SigmaCebir is a .NET desktop application I developed to explore the sigma-algebra concept algorithmically over finite sets. The user supplies a sample space and a family of subsets, and the program checks whether the family satisfies the required closure properties.
Mathematical Problem
A sigma-algebra contains the sample space and is closed under complement and countable union. For a finite sample space, those requirements can be checked through finite set operations.
The application was designed to provide more than a Boolean result. When the supplied family was incomplete, it could help expose which additional sets were required for closure.
Set Representation
The programming problem is not only the mathematical definition. Sets entered through a user interface need a canonical internal representation. Element ordering must not make mathematically equal sets appear different, duplicate values need to be normalized, and complement/union results must be comparable with the existing family.
Buttons for mathematical symbols made the input easier to express without changing the underlying set operations.
Retrospective
The project turned an abstract definition from probability theory into a validation algorithm. My later Probability and Statistics notes place sigma-algebras in their broader mathematical context.
The archived package size was 462 KB and the recorded MD5 was A48C77BF04F75AE336D382A4200FA7E5.
