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Let (Xm)∞1 be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X1., Xn) to converge in distribution, as n←∞ to a random variable with a uniform distribution on [0, 1).

Judd, JA orcid:0000-0001-8441-5008; Mccalman, JR orcid:0000-0002-3022-3980 ; Background: Health promotion by and with Aboriginal and Torres Strait Islander (hereafter Indigenous) Australians is critically important given a wide gap in health parity compared to other Australians. The development and implementation of step-by-step guides, instruments, packages, frameworks or resources has provided a feasible and low-resource strategy for strengthening evidence-informed health promotion practice. Yet there has been little assessment of where and how these tools are implemented or their effectiveness. This paper reviews the characteristics, implementation and effects of Indigenous health promotion tools. Methods. Indigenous health promotion tools were identified through a systematic literature search including a prior scoping study, eight databases, references of other reviews and the authors' knowledge (n = 1494). Documents in the peer reviewed and grey literature were included if they described or evaluated tools designed, recommended or used for strengthening Indigenous Australian health promotion. Eligible publications were entered into an Excel spreadsheet and documented tools classified according to their characteristics, implementation and effects. Quality was appraised using the Dictionary for Effective Public Health Practice Project (EPHPP) and Critical Appraisal Skills Program (CASP) tools for quantitative and qualitative studies respectively. Results: The review found that Indigenous health promotion tools were widely available. Of 74 publications that met inclusion criteria, sixty (81%) documented tools developed specifically for the Indigenous Australian population. All tools had been developed in reference to evidence; but only 22/74 (30%) publications specified intended or actual implementation, and only 11/74 (15%) publications evaluated impacts of the implemented tools. Impacts included health, environmental, community, organisational and health care improvements. The quality of impact evaluations was strong for only five (7%) studies. Conclusions: The small number and generally moderate quality of implementation and evaluation studies means that little is known about how tools work to strengthen Indigenous health promotion practice. The findings suggest that rather than continuing to invest in tool development, practitioners, policy makers and researchers could evaluate the implementation and effects of existing tools and publish the results. There is a need for long-term investment in research to review the current use of health promotion tools and the factors that are likely to enhance their implementation. © 2014 McCalman et al.; licensee BioMed Central Ltd. ; Associated Grant:Cooperative Research Centre for Aboriginal and Torres Strait Islander Health (CRCATSIH). The Cooperative Research Centres program is an Australian Government Initiative

OBJECTIVES:To examine barriers and facilitators to sustaining a sexual health continuous quality improvement (CQI) programme in clinics serving remote Aboriginal communities in Australia. DESIGN:Qualitative study. SETTING:Primary health care services serving remote Aboriginal communities in the Northern Territory, Australia. PARTICIPANTS:Seven of the 11 regional sexual health coordinators responsible for supporting the Northern Territory Government Remote Sexual Health Program. METHODS:Semi-structured in-depth interviews conducted in person or by telephone; data were analysed using an inductive and deductive thematic approach. RESULTS:Despite uniform availability of CQI tools and activities, sexual health CQI implementation varied across the Northern Territory. Participant narratives identified five factors enhancing the uptake and sustainability of sexual health CQI. At clinic level, these included adaptation of existing CQI tools for use in specific clinic contexts and risk environments (eg, a syphilis outbreak), local ownership of CQI processes and management support for CQI. At a regional level, factors included the positive framing of CQI as a tool to identify and act on areas for improvement, and regional facilitation of clinic level CQI activities. Three barriers were identified, including the significant workload associated with acute and chronic care in Aboriginal primary care services, high staff turnover and lack of Aboriginal staff. Considerations affecting the future sustainability of sexual health CQI included the need to reduce the burden on clinics from multiple CQI programmes, the contribution of regional sexual health coordinators and support structures, and access to and use of high-quality information systems. CONCLUSIONS:This study contributes to the growing evidence on how CQI approaches may improve sexual health in remote Australian Aboriginal communities. Enhancing sustainability of sexual health CQI in this context will require ongoing regional facilitation, efforts to build local ownership of CQI processes and management of competing demands on health service staff. ; Praveena Gunaratnam, Gill Schierhout, Jenny Brands, Lisa Maher, Ross Bailie, James Ward, Rebecca Guy, Alice Rumbold, Nathan Ryder, Christopher K Fairley, Basil Donovan, Liz Moore, John Kaldor, Stephen Bell

Objectives To examine barriers and facilitators to sustaining a sexual health continuous quality improvement (CQI) programme in clinics serving remote Aboriginal communities in Australia. Design Qualitative study. Setting Primary health care services serving remote Aboriginal communities in the Northern Territory, Australia. Participants Seven of the 11 regional sexual health coordinators responsible for supporting the Northern Territory Government Remote Sexual Health Program. Methods Semi-structured in-depth interviews conducted in person or by telephone; data were analysed using an inductive and deductive thematic approach. Results Despite uniform availability of CQI tools and activities, sexual health CQI implementation varied across the Northern Territory. Participant narratives identified five factors enhancing the uptake and sustainability of sexual health CQI. At clinic level, these included adaptation of existing CQI tools for use in specific clinic contexts and risk environments (eg, a syphilis outbreak), local ownership of CQI processes and management support for CQI. At a regional level, factors included the positive framing of CQI as a tool to identify and act on areas for improvement, and regional facilitation of clinic level CQI activities. Three barriers were identified, including the significant workload associated with acute and chronic care in Aboriginal primary care services, high staff turnover and lack of Aboriginal staff. Considerations affecting the future sustainability of sexual health CQI included the need to reduce the burden on clinics from multiple CQI programmes, the contribution of regional sexual health coordinators and support structures, and access to and use of high-quality information systems. Conclusions This study contributes to the growing evidence on how CQI approaches may improve sexual health in remote Australian Aboriginal communities. Enhancing sustainability of sexual health CQI in this context will require ongoing regional facilitation, efforts to build local ownership of CQI processes and management of competing demands on health service staff.