Finding a Published Research Paper Which Meaningfully Averages the Most Pathalogical Functions (v3)

I want to meaningfully average a pathalogical function (i.e., an everywhere surjective function whose graph has zero Hausdorff measure in its dimension). In case this impossible, we wish to average a nowhere continuous function defined on the rationals. We do this taking satisfying expected values of chosen sequences of bounded functions converging to f which are both equivalent and finite. As of now, I’m unable to solve this due to limited knowledge of advanced math and most people are too busy to help. Therefore, I’m wondering if anyone knows a research paper which solves my doubts. Unlike the previous paper, “Finding a Research Paper Which Meaningfully Averages Pathalogical Functions (V2)" [1] we modified the equations, the theorems, the approach to solving theorems in the blockquote, and the leading question which solves the blockquote. We also deleted unnecessary definitions to make the paper less complicated.