Acknowledgements ................................................ 3
1 Introduction ................................................. 5
2 Preliminaries ............................................... 11
2.1 Slices and intersection measures ....................... 12
2.2 Dimensions of measures ................................. 13
3 Similarities ................................................ 16
3.1 Properties of intersection measures .................... 16
3.2 Local dimensions of intersection measures .............. 21
3.3 Hausdorff and packing dimensions of intersection
measures ............................................... 34
3.4 Average dimensions ..................................... 37
4 Linear maps and continuously differentiable functions ....... 40
4.1 Properties of intersection measures .................... 41
4.2 Local dimensions of intersection measures .............. 44
4.3 Hausdorff, packing and average dimensions .............. 50
References ..................................................... 52
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