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We investigate multifractal regularity for infinite conformal iteratedfunction systems (cIFS). That is we determine to what extent the multifractalspectrum depends continuously on the cIFS and its thermodynamic potential. Forthis we introduce the notion of regular convergence for families of cIFS notnecessarily sharing the same index set, which guarantees the convergence of themultifractal spectra on the interior of their domain. In particular, we obtainan Exhausting Principle for infinite cIFS allowing us to carry over results forfinite to infinite systems, and in this way to establish a multifractalanalysis without the usual regularity conditions. Finally, we discuss theconnections to the $\lambda$-topology introduced by Roy and Urbas{\'n}ki.

Regularity of multifractal spectra of conformal iterated function systems