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The finite cardinalities of level sets of the Takagi function
Takagi function Nowhere-differentiable function Level set Self-similarity Takagi expansion
2011/8/25
Abstract: Let T be Takagi's continuous but nowhere-differentiable function. It is known that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. We show that the mos...
Level Sets of the Takagi Function: Local Level Sets
Level Sets Takagi Function Local Level Sets
2010/11/30
The Takagi function : [0; 1] ! [0; 1] is a continuous non-di erentiable functio constructed
by Takagi in 1903. This paper studies the level sets L(y) = fx : (x) = yg of the Takagi
function (x)...
Level Sets of the Takagi Function: Generic Level Sets
the Takagi Function Generic Level Sets
2010/11/19
The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. This paper studies the level sets L(y) = {x : \tau (x) = y} of the Takagi funct...