This book comes in two parts; the first, consisting of §§1–7, offers an informal axiomatic introduction to the basics of set theory, including a thorough discussion of the axiom of choice and some of its equivalents. The second part, consisting of §§8–14, is written at a somewhat more advanced level, and treats selected topics in transfinite algebra; that is, algebraic themes where the axiom of choice, in one form or another, is useful or even indispensable.

This chapter is devoted to presenting some basic results concerning the differential structure on an arbitrary metric space. By a metric measure space, we mean a complete and separable metric space equipped with a non-zero non-negative Borel measure which is finite on bounded sets. In the literature, there are several possible definitions of Sobolev spaces in this setting, most prominently via p-upper gradients, p-relaxed slopes, and via test plans. Under minimal assumptions, all these definitions agree; we present these equivalent approaches in Appendix B and now introduce the most suitable definition for our purposes: the Newtonian space. We also present the definition of functions of bounded variation, their main properties, and discuss how to define the boundary measure of a set of finite perimeter and the relationships between them. In the second half of this chapter, we present the theory of Lp-normed modules and the first-order differential structure on metric measure spaces introduced by Gigli. We also recall the definition of divergence in the metric setting and discuss how to adapt these notions to the case of a sufficiently regular open subset of a metric measure space.

Chapter 2 explores how Bourbon supporters vied for public attention amid a swirl of conflicting news, persistent rumors, and the threat of pro-Habsburg dissent. It reconstructs a “Baroque public sphere” where print culture, spectacle, and oratory intersected with popular engagement. Bourbon officials and clergy used relaciones de suceso (news pamphlets), popular imprints, and sermons to broadcast pro-Bourbon messages, repurposing reports from Spain to cultivate loyalty and reinforce imperial unity in New Spain. Despite censorship, Habsburg sympathizers circulated subversive ideas, often cloaked in coded language. Disloyalty investigations in Mexico City uncover the strategies subjects used to signal political leanings while evading punishment. By tracing how print and oral propaganda moved across space and audiences—absorbed, repeated, contested—this chapter shows how actors across the empire helped construct a shared narrative of Bourbon legitimacy. The imagined community of empire emerged not passively but through conscious engagement with competing voices.

Making decisions about prescribing medication for mental disorders in childbearing women is a task that may have profound and long-lasting implications for a mother and her family, and it is important that prescribers have access to up-to-date summaries and interpretations of research that examines how safe these medications are in pregnancy and lactation.

Because it is not possible to test a drug’s reproductive safety in randomised controlled trials, research has to rely on less rigorous study designs. The inherent difficulties and other methodological problems have meant that interpretation of the evidence has often been difficult. However, the volume and quality of research has dramatically increased in recent years. Current findings concerning antidepressant, antipsychotic and mood-stabilising medication during pregnancy and lactation are summarised in this chapter, and recommendations for clinical practice are made referring to published guidelines where they are available.

Relative clauses are generally introduced in the archaic Indo-European languages by a relative pronoun. In some languages, this pronoun is descended from a form *kwí-/*kwó-, while in others it is descended from a form *yó-. This chapter surveys the syntactic and semantic behaviour of the descendants of these pronouns in the attested languages. This includes a discussion of both their relative and non-relative uses. The author concludes that neither *kwí-/*kwó- nor *yó- can be excluded as a relative pronoun in Proto-Indo- European, and that together they reflect what was a unitary syntactic category in the proto-language: *REL.

This chapter examines recent evidence concerning the need to explicitly intervene with the mother-infant dyad in order to ensure optimal outcomes for the infant where there are concerns about postnatal mental health problems. The chapter describes the importance of dyadic interaction in terms of the capacity of the infant for later affect regulation and wider aspects of development, in addition to evidence concerning the impact of perinatal mental health problems on such interaction. A number of different methods of assessing mother-infant interaction in order to identify whether an intervention is needed are described, in addition to a range of dyadic methods of working that are explicitly focused on improving the interaction.

Provincial governance was never of great interest to Roman administrators or jurists. This begins to change only when jurists increasingly became administrators exposed to provincial claim. Jurists had to begin thinking about provincial contexts as raising important questions of governance - in particular, that key assumptions about law might be different in a world marked by extractive governance. Key among these is the late second/early third century jurist Ulpian of Tyre. Ulpian begins the process of transforming governance from an array of untheorized practices into something amenable to traditional juristic analysis. As a successful administrator, he did this knowing that such an account was otherwise lacking. His magnum opus, On the Office of the Proconsul, can be seen as an attempt to capture what was distinctly provincial about provincial governance. But Ulpian’s key text can also be read as a response to the challenge of provincial legalism.

Criminal punishment captured the imagination. It was a violent process, staged deliberately by the state to demonstrate certain truths about state power. However, these public scenes were susceptible to rewriting by provincial subjects. These subjects fixated on state attempts to define truth by means of judicial violence. Subjects insisted that violence be conditioned on its respect for provincial logos - rational discussions about the nature of any particular act of state violence. They emphasized that the courtroom (rather than the archive) was the most important locus for determining the content of laws and the boundaries of state power and insisted that the courtroom be a space not just for punishment, but communication. Most prolific on this point are early Christian writings about martyrs, which emphasized what they claimed was the Roman state’s incapacity to rationally defend the persecution of Christians. It is found among Jews and pagans as well.

This chapter reconstructs some principal features of relative clause syntax in Proto-Indo-European. Following the methodology outlined in Chapter 2, it pays close attention to the behaviour of the reconstructed relative pronoun, *REL (Chapter 4), and its position in the PIE left periphery (Chapter 5). Moving away from *REL, it then turns to the more general structures of, and relations between, ‘plain’ relative and correlative clauses in PIE. The chapter is rounded off by a discussion regarding the semantic types of relative clauses in PIE and their syntactic form.

This book comes in two parts; the first, consisting of §§1–7, offers an informal axiomatic introduction to the basics of set theory, including a thorough discussion of the axiom of choice and some of its equivalents. The second part, consisting of §§8–14, is written at a somewhat more advanced level, and treats selected topics in transfinite algebra; that is, algebraic themes where the axiom of choice, in one form or another, is useful or even indispensable.

Violence is central to popular images of the Middle Ages. Where do clergy fit into this picture? In theory, they were meant to oppose violence and promote peace. But in practice, clergy sometimes took part in warfare. Recent scholarship shows that clergy even engaged in interpersonal violence, and this book pursues this theme further. It will draw on approaches from anthropology, gender and the ‘history of emotions’, which ask fundamental questions: What is violence? How can it be defined as legitimate or illegitimate? Is it innate or learnt behaviour? What purposes does it serve? How far is it gendered? What motivated it? And was the Middle Ages more violent than the present? In applying these approaches, the book seeks to understand how far clergy were separate from the violent culture of laymen around them. Various sources will be used to answer this central question, notably the papal penitentiary registers, church and secular court records and canon law. Legal theory sought to set clergy apart from laymen especially regarding violent crime, so the book will seek to compare this with judicial practice. It thus constitutes a study in legal and social history.

The perinatal frame of mind is a concept aiming to capture the unique mental state, context and experiences of individuals planning a pregnancy and during the perinatal period. It implies that every aspect of the physical, social, psychological and psychiatric care of women in this period requires a deep understanding of them as individuals. This encompasses many aspects of a woman’s life experience: from childhood to her current context, including traumatic and more positive experiences, cultural factors, relationships, mental and physical illness and their risks and relevance to the perinatal context, her journey to becoming pregnant, and her strengths. The term asks that we think not only about the woman, her well-being and needs, but also those of the fetus or infant, the intimate partner and/or co-parent, and other family members. We should consider the relationships between the parents and the infant, as well as within the couple and among other family members. So, we don’t just think about the woman, but the community and cultural context surrounding her, which includes the partner, family, friends, and often, and importantly, health and social professionals and services, who can provide the right kind of support to help navigate any mental health challenges.