On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Safety risks among frail older people living at home in the Netherlands:A cross‐sectional study in a routine primary care sample

Frail older people face a range of problems and risks that could undermine their ability to live safely at home. A comprehensive overview of these risks, from a multidimensional perspective, is currently lacking. This study aims to examine the prevalence of risks in multiple domains of life among frail older people living at home. We used cross‐sectional data from 824 people aged 65 years and older, who received a comprehensive geriatric assessment (the interRAI Home Care [interRAI‐HC]) between 2014 and 2018, as part of routine care from 25 general practices in the region of West‐Friesland, the Netherlands. The interRAI‐HC identifies amenable risks related to people's clinical conditions, functioning, lifestyle and behaviour, and social and physical environment. Descriptive statistics were used to examine population characteristics (age, gender, marital status, living arrangements and presence of chronic conditions) and prevalence of risks. Most common risks were related to people's clinical conditions (i.e cardio‐respiratory health, urinary incontinence, pain), functioning (i.e. limitations in instrumental activities of daily living and mood) and social environment (i.e. limitations in informal care and social functioning). More than 80% of frail older people faced multiple risks, and often on multiple domains of life simultaneously. People experiencing multiple risks per person, and on multiple domains simultaneously, were more often widowed and living alone. The multidimensional character of risks among frail older people living at home implies that an integrated approach to care, comprising both health and social care, is necessary. Insight in the prevalence of these risks can give direction to care allocation decisions

Ds C Spoelstra en die Nederduitsch Hervormde Kerk

Rev C Spoelstra and the Nederduitsch Hervormde Kerk. The inter relationship between 'Rev C Spoelstra and the Nederduitsch Hervormde Kerk' is studies from three different perspectives: Spoelstra with or as part of the church (a positive relationship). Secondly, there is the increasing tension between Spoelstra and Rev M J Goddefroy (Goddefroy eventually became to  Spoelstra the representation of the whole Nederduitsch Hervonnde Kerk). Thirdly, Spoelstra opposed the whole Nederduitsch Hervormde Kerk and not only Goddefroy