Hausdorff measure and level sets of typical continuous mappings in Euclidean spaces
Hausdorff measure and level sets of typical continuous mappings in Euclidean spaces
We determine the Hausdorff dimension of level sets and of sets of points of multiplicity for mappings in a residual subset of the space of all continuous mappings from <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> …