Finitely Additive Measure Necessity Without Set-Theoretic Assumptions

Computational evidence for CA-FA total variation distance gaps via partition refinement

0.0554
Peak Mean Gap (n=16)
0.1179
Max Single Gap
32.08x
Max Hull Expansion
99%
Weak-* Positive Rate

CA-FA Total Variation Gap

Convex Hull Expansion Ratio

TV Distances: CA vs FA

Weak-* Closure Gap

Detailed Results

nTV_CATV_FAGap (mean)Gap (max)Hull Ratio
40.02100.00190.01910.09361.298
80.05160.03090.02070.04971.114
160.27760.22210.05540.11791.765
320.34840.29510.05330.10642.185
640.39280.34820.04460.072825.381
1280.42580.40200.02380.045432.080
2560.43890.42210.01670.0397-
5120.46050.45250.00790.0193-