informationvolume

Informationvolume is a proposed metric intended to quantify the total informational content within a bounded region of a data space. It aims to merge information density with a geometric notion of volume, producing a scalar that reflects how much information is represented by, or needed to describe, objects drawn from that region. The concept is not standard in mainstream theory and is mainly discussed in theoretical contexts.

Formally, for a space with probability density p(x) and a measurable region R, one informal definition is V(R) = ∫_R p(x) log2(1/p(x)) dμ(x). This can be read as the region-weighted self-information of outcomes in R, roughly the information required to describe events falling inside R, weighted by their likelihood.

Informationvolume is related to entropy and Kolmogorov complexity but is not identical to either. It depends on the chosen model and region, and is not generally computable for arbitrary spaces.

Potential uses include comparing datasets, guiding data compression heuristics, and analyzing information flow in networks, by highlighting regions with high informative value relative to their size.

Limitations include model dependency, sensitivity to coordinate choices, and the lack of standardized definitions. As a concept, informationvolume remains informal in many contexts and is best used as a heuristic tool alongside established measures such as entropy and Kolmogorov complexity.