Income tax: is income to which Australia has no taxing right, because of a double tax agreement but which is also exempt from tax under sections 23AF or 23AG of the Income Tax Assessment Act 1936, included in the 'exempt amount' for the purpose of the exemption with progression calculation?

No. The references in subsections 23AF(17A) and 23AG(3) to "an amount that is exempt from tax under this section" apply in respect of income that only qualifies for exemption by reason of sections 23AF or 23AG and not for any other reason. Example An Australian resident renders service to the Swedish Government. The service is performed in Sweden. The service constitutes "foreign service for a continuous period of not less than 91 days" as required by subsection 23AG(1). Article 19 of the Sweden/Australia Double Tax Agreement allocates to Sweden the sole taxing right over any remuneration received in respect of this service. This remuneration will not be taken into account for the purposes of the calculation of Australian tax payable on other income.