# Heuristic and computer calculations for the magnitude of metric spaces

@inproceedings{Willerton2009HeuristicAC, title={Heuristic and computer calculations for the magnitude of metric spaces}, author={Simon Willerton}, year={2009} }

The notion of the magnitude of a compact metric space was considered in arXiv:0908.1582 with Tom Leinster, where the magnitude was calculated for line segments, circles and Cantor sets. In this paper more evidence is presented for a conjectured relationship with a geometric measure theoretic valuation. Firstly, a heuristic is given for deriving this valuation by considering 'large' subspaces of Euclidean space and, secondly, numerical approximations to the magnitude are calculated for squares… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## The magnitude of metric spaces

VIEW 4 EXCERPTS

CITES RESULTS & BACKGROUND

HIGHLY INFLUENCED

## Positive definite metric spaces

VIEW 7 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## THE MAGNITUDE OF A METRIC SPACE: FROM CATEGORY THEORY TO GEOMETRIC MEASURE THEORY

VIEW 3 EXCERPTS

CITES RESULTS & METHODS

## Magnitude, Diversity, Capacities, and Dimensions of Metric Spaces

VIEW 6 EXCERPTS

CITES BACKGROUND & RESULTS

HIGHLY INFLUENCED

## Notions of M\"obius inversion

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-5 OF 5 REFERENCES

## Introduction to Geometric Probability

VIEW 3 EXCERPTS

## Measuring biological diversity

VIEW 1 EXCERPT

## Curvature measures

VIEW 2 EXCERPTS

## Life in the Freezer, BBC television documentary, Episode 5, The Big Freeze, 1993

VIEW 1 EXCERPT

## Metric spaces, post at The n-Category Café

VIEW 1 EXCERPT